How do I find the distance from a point to a plane?
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I am trying to find the distance from point $(8, 0, -6)$ and plane $x+y+z = 6$. I tried solving it but I am still getting it wrong. Can anyone help me on this? Any help I would very much appreciate.
The following is my work:
$$d = sqrt{(x-8)^2 + (y-0)^2 + (z+6)^2}$$
since $x+y+z = 6$, $z = 6-x-y$, so
begin{align*}
d &= sqrt{(x-8)^2 + (y-0)^2 + (-x-y+12)^2} \
d^2 &= (x-8)^2 + (y-0)^2 + (-x-y)^2
end{align*}
Find partial derivative $f_x$ and $f_y$ and critical points
begin{align*}
f_x &= 2(x-8) + 2(-x-y+12) \
&= 24-2y quad (text{set }= 0) \
&= text{critical point }y = 4 \
f_y &= 2y + 2(-x-y+12) \
&= 24 - 2x quad (text{set }= 0) \
&= text{critical point }x = 12 \
end{align*}
Plug in $x = 12$ and $y = 4$ to original equation
$$d = sqrt{(x - 8)^2 + (4)^2 + (-12-4+12)^2} = sqrt{48}$$
multivariable-calculus optimization cauchy-schwarz-inequality
$endgroup$
add a comment |
$begingroup$
I am trying to find the distance from point $(8, 0, -6)$ and plane $x+y+z = 6$. I tried solving it but I am still getting it wrong. Can anyone help me on this? Any help I would very much appreciate.
The following is my work:
$$d = sqrt{(x-8)^2 + (y-0)^2 + (z+6)^2}$$
since $x+y+z = 6$, $z = 6-x-y$, so
begin{align*}
d &= sqrt{(x-8)^2 + (y-0)^2 + (-x-y+12)^2} \
d^2 &= (x-8)^2 + (y-0)^2 + (-x-y)^2
end{align*}
Find partial derivative $f_x$ and $f_y$ and critical points
begin{align*}
f_x &= 2(x-8) + 2(-x-y+12) \
&= 24-2y quad (text{set }= 0) \
&= text{critical point }y = 4 \
f_y &= 2y + 2(-x-y+12) \
&= 24 - 2x quad (text{set }= 0) \
&= text{critical point }x = 12 \
end{align*}
Plug in $x = 12$ and $y = 4$ to original equation
$$d = sqrt{(x - 8)^2 + (4)^2 + (-12-4+12)^2} = sqrt{48}$$
multivariable-calculus optimization cauchy-schwarz-inequality
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$begingroup$
How did the $6$ become the $12$?
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– Theo Bendit
Feb 24 at 4:21
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because z = - x - y + 6. So since I plug in (z + 6)^2 in the distance formula, it becomes (-x - y + 12)^2
$endgroup$
– Niko
Feb 24 at 4:25
add a comment |
$begingroup$
I am trying to find the distance from point $(8, 0, -6)$ and plane $x+y+z = 6$. I tried solving it but I am still getting it wrong. Can anyone help me on this? Any help I would very much appreciate.
The following is my work:
$$d = sqrt{(x-8)^2 + (y-0)^2 + (z+6)^2}$$
since $x+y+z = 6$, $z = 6-x-y$, so
begin{align*}
d &= sqrt{(x-8)^2 + (y-0)^2 + (-x-y+12)^2} \
d^2 &= (x-8)^2 + (y-0)^2 + (-x-y)^2
end{align*}
Find partial derivative $f_x$ and $f_y$ and critical points
begin{align*}
f_x &= 2(x-8) + 2(-x-y+12) \
&= 24-2y quad (text{set }= 0) \
&= text{critical point }y = 4 \
f_y &= 2y + 2(-x-y+12) \
&= 24 - 2x quad (text{set }= 0) \
&= text{critical point }x = 12 \
end{align*}
Plug in $x = 12$ and $y = 4$ to original equation
$$d = sqrt{(x - 8)^2 + (4)^2 + (-12-4+12)^2} = sqrt{48}$$
multivariable-calculus optimization cauchy-schwarz-inequality
$endgroup$
I am trying to find the distance from point $(8, 0, -6)$ and plane $x+y+z = 6$. I tried solving it but I am still getting it wrong. Can anyone help me on this? Any help I would very much appreciate.
The following is my work:
$$d = sqrt{(x-8)^2 + (y-0)^2 + (z+6)^2}$$
since $x+y+z = 6$, $z = 6-x-y$, so
begin{align*}
d &= sqrt{(x-8)^2 + (y-0)^2 + (-x-y+12)^2} \
d^2 &= (x-8)^2 + (y-0)^2 + (-x-y)^2
end{align*}
Find partial derivative $f_x$ and $f_y$ and critical points
begin{align*}
f_x &= 2(x-8) + 2(-x-y+12) \
&= 24-2y quad (text{set }= 0) \
&= text{critical point }y = 4 \
f_y &= 2y + 2(-x-y+12) \
&= 24 - 2x quad (text{set }= 0) \
&= text{critical point }x = 12 \
end{align*}
Plug in $x = 12$ and $y = 4$ to original equation
$$d = sqrt{(x - 8)^2 + (4)^2 + (-12-4+12)^2} = sqrt{48}$$
multivariable-calculus optimization cauchy-schwarz-inequality
multivariable-calculus optimization cauchy-schwarz-inequality
edited Feb 24 at 4:32
Michael Rozenberg
109k1896201
109k1896201
asked Feb 24 at 4:13
NikoNiko
184
184
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How did the $6$ become the $12$?
$endgroup$
– Theo Bendit
Feb 24 at 4:21
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because z = - x - y + 6. So since I plug in (z + 6)^2 in the distance formula, it becomes (-x - y + 12)^2
$endgroup$
– Niko
Feb 24 at 4:25
add a comment |
$begingroup$
How did the $6$ become the $12$?
$endgroup$
– Theo Bendit
Feb 24 at 4:21
$begingroup$
because z = - x - y + 6. So since I plug in (z + 6)^2 in the distance formula, it becomes (-x - y + 12)^2
$endgroup$
– Niko
Feb 24 at 4:25
$begingroup$
How did the $6$ become the $12$?
$endgroup$
– Theo Bendit
Feb 24 at 4:21
$begingroup$
How did the $6$ become the $12$?
$endgroup$
– Theo Bendit
Feb 24 at 4:21
$begingroup$
because z = - x - y + 6. So since I plug in (z + 6)^2 in the distance formula, it becomes (-x - y + 12)^2
$endgroup$
– Niko
Feb 24 at 4:25
$begingroup$
because z = - x - y + 6. So since I plug in (z + 6)^2 in the distance formula, it becomes (-x - y + 12)^2
$endgroup$
– Niko
Feb 24 at 4:25
add a comment |
6 Answers
6
active
oldest
votes
$begingroup$
Your approach is a good one, and in fact can lead to the general formula mentioned in the other answers.
You just made a few mistakes in your calculation.
For example, you say that $frac{partial}{partial x} left[ (x-8)^2+y^2+(-x-y+12)^2 right]$ is $2(x-8)+2(-x-y+12)$, when really it is $2(x-8)-2(-x-y-12)$. You forgot the chain rule.
You make a similar chain rule mistake when calculating the partial derivative with respect to $y$.
I think if you fix these, you should be able to finish your calculation the way you started it.
Note to other posters: I think it is generally of greater pedagogical value to help a student realize how to fix their own reasoning, rather than supplying them with a totally different method. Our primary aim should be to empower students to realize that they have the power to think through these things logically and creatively.
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+1 for fixing the error in the - otherwise correct - OP's solution.
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– Pere
Feb 24 at 14:13
add a comment |
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The distance formula is $$D=frac{|ax_0+by_0 +cz_0-d|}{sqrt{a^2+b^2+c^2}}=frac{4}{sqrt3}.$$
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add a comment |
$begingroup$
The closest distance will be along a line perpendicular to the plane or parallel to $(1,1,1)$. Since $8+0+-6=2$ we must add $frac{4}{3}$ to each component so that $x+y+z$ now equals $6$. Therefore, the distance is $|(frac{4}{3}, frac{4}{3}, frac{4}{3})|=sqrt{3frac{16}{9}}=sqrt{frac{16}{3}}=frac{4}{sqrt{3}}$
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add a comment |
$begingroup$
It's $$frac{|8+0-6-6|}{sqrt{1^2+1^2+1^2}}=frac{4}{sqrt3}.$$
I used the following formula.
The distance from the point $(x_1,y_1,z_1)$ to the plane $ax+by+cz+d=0$ it's
$$frac{|ax_1+by_1+cz_1+d|}{sqrt{a^2+b^2+c^2}}.$$
Also, we can end your way.
Indeed, by C-S
$$sqrt{(x-8)^2+y^2+(z+6)^2}=frac{1}{sqrt3}sqrt{(1^2+1^2+1^2)((x-8)^2+y^2+(z+6)^2)}geq$$
$$geqfrac{1}{sqrt3}sqrt{(x-8+y+z+6)^2}=frac{4}{sqrt3}$$ and we got the distance again.
$endgroup$
$begingroup$
thank you very much! this I smuch quicker than what I am being told to do
$endgroup$
– Niko
Feb 24 at 4:24
add a comment |
$begingroup$
Option:
Normal of the plane: $(1,1,1)$,
Normalized(i.e of unit length): $(1/√3)(1,1,1)$
Line through $(8,0,-6)$:
$vec r= (8,0,-6)+t (1/√3)(1,1,1)$.
Determine $t$ when line intersects plane:
$(8+t/√3)+t/√3+(-6+t/√3)=6;$
$3(t/√3)=4$;
$t= 4/√3.$
Distance = $4/√3$ (Why?).
$endgroup$
$begingroup$
Very nice application of vector algebra (+1). The answer could be improved by explicitly citing that the coefficients of the variables in the plane equations are the component of a vector orthogonal to the plane. And also answering the last "why?" could improve it. The OP (or other people reading the answer) might not be aware of this application of vector algebra. This answer would need a nice drawing to be great!
$endgroup$
– Lorenzo Donati
Feb 24 at 11:37
$begingroup$
Lorenzo.Thanks.If you feel any edits would be in place, feel free. This answer is an option, a bit of a different approach ,not just calculating a root, etc.Thank you again for your kind words.Greetings, Peter
$endgroup$
– Peter Szilas
Feb 24 at 13:31
add a comment |
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You can draw a line from your point to the plane and then find the length of its projection onto the unit normal vector to the plane.
$endgroup$
add a comment |
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6 Answers
6
active
oldest
votes
6 Answers
6
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your approach is a good one, and in fact can lead to the general formula mentioned in the other answers.
You just made a few mistakes in your calculation.
For example, you say that $frac{partial}{partial x} left[ (x-8)^2+y^2+(-x-y+12)^2 right]$ is $2(x-8)+2(-x-y+12)$, when really it is $2(x-8)-2(-x-y-12)$. You forgot the chain rule.
You make a similar chain rule mistake when calculating the partial derivative with respect to $y$.
I think if you fix these, you should be able to finish your calculation the way you started it.
Note to other posters: I think it is generally of greater pedagogical value to help a student realize how to fix their own reasoning, rather than supplying them with a totally different method. Our primary aim should be to empower students to realize that they have the power to think through these things logically and creatively.
$endgroup$
$begingroup$
+1 for fixing the error in the - otherwise correct - OP's solution.
$endgroup$
– Pere
Feb 24 at 14:13
add a comment |
$begingroup$
Your approach is a good one, and in fact can lead to the general formula mentioned in the other answers.
You just made a few mistakes in your calculation.
For example, you say that $frac{partial}{partial x} left[ (x-8)^2+y^2+(-x-y+12)^2 right]$ is $2(x-8)+2(-x-y+12)$, when really it is $2(x-8)-2(-x-y-12)$. You forgot the chain rule.
You make a similar chain rule mistake when calculating the partial derivative with respect to $y$.
I think if you fix these, you should be able to finish your calculation the way you started it.
Note to other posters: I think it is generally of greater pedagogical value to help a student realize how to fix their own reasoning, rather than supplying them with a totally different method. Our primary aim should be to empower students to realize that they have the power to think through these things logically and creatively.
$endgroup$
$begingroup$
+1 for fixing the error in the - otherwise correct - OP's solution.
$endgroup$
– Pere
Feb 24 at 14:13
add a comment |
$begingroup$
Your approach is a good one, and in fact can lead to the general formula mentioned in the other answers.
You just made a few mistakes in your calculation.
For example, you say that $frac{partial}{partial x} left[ (x-8)^2+y^2+(-x-y+12)^2 right]$ is $2(x-8)+2(-x-y+12)$, when really it is $2(x-8)-2(-x-y-12)$. You forgot the chain rule.
You make a similar chain rule mistake when calculating the partial derivative with respect to $y$.
I think if you fix these, you should be able to finish your calculation the way you started it.
Note to other posters: I think it is generally of greater pedagogical value to help a student realize how to fix their own reasoning, rather than supplying them with a totally different method. Our primary aim should be to empower students to realize that they have the power to think through these things logically and creatively.
$endgroup$
Your approach is a good one, and in fact can lead to the general formula mentioned in the other answers.
You just made a few mistakes in your calculation.
For example, you say that $frac{partial}{partial x} left[ (x-8)^2+y^2+(-x-y+12)^2 right]$ is $2(x-8)+2(-x-y+12)$, when really it is $2(x-8)-2(-x-y-12)$. You forgot the chain rule.
You make a similar chain rule mistake when calculating the partial derivative with respect to $y$.
I think if you fix these, you should be able to finish your calculation the way you started it.
Note to other posters: I think it is generally of greater pedagogical value to help a student realize how to fix their own reasoning, rather than supplying them with a totally different method. Our primary aim should be to empower students to realize that they have the power to think through these things logically and creatively.
answered Feb 24 at 13:56
Steven GubkinSteven Gubkin
5,7291531
5,7291531
$begingroup$
+1 for fixing the error in the - otherwise correct - OP's solution.
$endgroup$
– Pere
Feb 24 at 14:13
add a comment |
$begingroup$
+1 for fixing the error in the - otherwise correct - OP's solution.
$endgroup$
– Pere
Feb 24 at 14:13
$begingroup$
+1 for fixing the error in the - otherwise correct - OP's solution.
$endgroup$
– Pere
Feb 24 at 14:13
$begingroup$
+1 for fixing the error in the - otherwise correct - OP's solution.
$endgroup$
– Pere
Feb 24 at 14:13
add a comment |
$begingroup$
The distance formula is $$D=frac{|ax_0+by_0 +cz_0-d|}{sqrt{a^2+b^2+c^2}}=frac{4}{sqrt3}.$$
$endgroup$
add a comment |
$begingroup$
The distance formula is $$D=frac{|ax_0+by_0 +cz_0-d|}{sqrt{a^2+b^2+c^2}}=frac{4}{sqrt3}.$$
$endgroup$
add a comment |
$begingroup$
The distance formula is $$D=frac{|ax_0+by_0 +cz_0-d|}{sqrt{a^2+b^2+c^2}}=frac{4}{sqrt3}.$$
$endgroup$
The distance formula is $$D=frac{|ax_0+by_0 +cz_0-d|}{sqrt{a^2+b^2+c^2}}=frac{4}{sqrt3}.$$
answered Feb 24 at 4:23
Mohammad Riazi-KermaniMohammad Riazi-Kermani
41.6k42061
41.6k42061
add a comment |
add a comment |
$begingroup$
The closest distance will be along a line perpendicular to the plane or parallel to $(1,1,1)$. Since $8+0+-6=2$ we must add $frac{4}{3}$ to each component so that $x+y+z$ now equals $6$. Therefore, the distance is $|(frac{4}{3}, frac{4}{3}, frac{4}{3})|=sqrt{3frac{16}{9}}=sqrt{frac{16}{3}}=frac{4}{sqrt{3}}$
$endgroup$
add a comment |
$begingroup$
The closest distance will be along a line perpendicular to the plane or parallel to $(1,1,1)$. Since $8+0+-6=2$ we must add $frac{4}{3}$ to each component so that $x+y+z$ now equals $6$. Therefore, the distance is $|(frac{4}{3}, frac{4}{3}, frac{4}{3})|=sqrt{3frac{16}{9}}=sqrt{frac{16}{3}}=frac{4}{sqrt{3}}$
$endgroup$
add a comment |
$begingroup$
The closest distance will be along a line perpendicular to the plane or parallel to $(1,1,1)$. Since $8+0+-6=2$ we must add $frac{4}{3}$ to each component so that $x+y+z$ now equals $6$. Therefore, the distance is $|(frac{4}{3}, frac{4}{3}, frac{4}{3})|=sqrt{3frac{16}{9}}=sqrt{frac{16}{3}}=frac{4}{sqrt{3}}$
$endgroup$
The closest distance will be along a line perpendicular to the plane or parallel to $(1,1,1)$. Since $8+0+-6=2$ we must add $frac{4}{3}$ to each component so that $x+y+z$ now equals $6$. Therefore, the distance is $|(frac{4}{3}, frac{4}{3}, frac{4}{3})|=sqrt{3frac{16}{9}}=sqrt{frac{16}{3}}=frac{4}{sqrt{3}}$
answered Feb 24 at 4:27
John DoumaJohn Douma
5,66011520
5,66011520
add a comment |
add a comment |
$begingroup$
It's $$frac{|8+0-6-6|}{sqrt{1^2+1^2+1^2}}=frac{4}{sqrt3}.$$
I used the following formula.
The distance from the point $(x_1,y_1,z_1)$ to the plane $ax+by+cz+d=0$ it's
$$frac{|ax_1+by_1+cz_1+d|}{sqrt{a^2+b^2+c^2}}.$$
Also, we can end your way.
Indeed, by C-S
$$sqrt{(x-8)^2+y^2+(z+6)^2}=frac{1}{sqrt3}sqrt{(1^2+1^2+1^2)((x-8)^2+y^2+(z+6)^2)}geq$$
$$geqfrac{1}{sqrt3}sqrt{(x-8+y+z+6)^2}=frac{4}{sqrt3}$$ and we got the distance again.
$endgroup$
$begingroup$
thank you very much! this I smuch quicker than what I am being told to do
$endgroup$
– Niko
Feb 24 at 4:24
add a comment |
$begingroup$
It's $$frac{|8+0-6-6|}{sqrt{1^2+1^2+1^2}}=frac{4}{sqrt3}.$$
I used the following formula.
The distance from the point $(x_1,y_1,z_1)$ to the plane $ax+by+cz+d=0$ it's
$$frac{|ax_1+by_1+cz_1+d|}{sqrt{a^2+b^2+c^2}}.$$
Also, we can end your way.
Indeed, by C-S
$$sqrt{(x-8)^2+y^2+(z+6)^2}=frac{1}{sqrt3}sqrt{(1^2+1^2+1^2)((x-8)^2+y^2+(z+6)^2)}geq$$
$$geqfrac{1}{sqrt3}sqrt{(x-8+y+z+6)^2}=frac{4}{sqrt3}$$ and we got the distance again.
$endgroup$
$begingroup$
thank you very much! this I smuch quicker than what I am being told to do
$endgroup$
– Niko
Feb 24 at 4:24
add a comment |
$begingroup$
It's $$frac{|8+0-6-6|}{sqrt{1^2+1^2+1^2}}=frac{4}{sqrt3}.$$
I used the following formula.
The distance from the point $(x_1,y_1,z_1)$ to the plane $ax+by+cz+d=0$ it's
$$frac{|ax_1+by_1+cz_1+d|}{sqrt{a^2+b^2+c^2}}.$$
Also, we can end your way.
Indeed, by C-S
$$sqrt{(x-8)^2+y^2+(z+6)^2}=frac{1}{sqrt3}sqrt{(1^2+1^2+1^2)((x-8)^2+y^2+(z+6)^2)}geq$$
$$geqfrac{1}{sqrt3}sqrt{(x-8+y+z+6)^2}=frac{4}{sqrt3}$$ and we got the distance again.
$endgroup$
It's $$frac{|8+0-6-6|}{sqrt{1^2+1^2+1^2}}=frac{4}{sqrt3}.$$
I used the following formula.
The distance from the point $(x_1,y_1,z_1)$ to the plane $ax+by+cz+d=0$ it's
$$frac{|ax_1+by_1+cz_1+d|}{sqrt{a^2+b^2+c^2}}.$$
Also, we can end your way.
Indeed, by C-S
$$sqrt{(x-8)^2+y^2+(z+6)^2}=frac{1}{sqrt3}sqrt{(1^2+1^2+1^2)((x-8)^2+y^2+(z+6)^2)}geq$$
$$geqfrac{1}{sqrt3}sqrt{(x-8+y+z+6)^2}=frac{4}{sqrt3}$$ and we got the distance again.
edited Feb 24 at 4:28
answered Feb 24 at 4:17
Michael RozenbergMichael Rozenberg
109k1896201
109k1896201
$begingroup$
thank you very much! this I smuch quicker than what I am being told to do
$endgroup$
– Niko
Feb 24 at 4:24
add a comment |
$begingroup$
thank you very much! this I smuch quicker than what I am being told to do
$endgroup$
– Niko
Feb 24 at 4:24
$begingroup$
thank you very much! this I smuch quicker than what I am being told to do
$endgroup$
– Niko
Feb 24 at 4:24
$begingroup$
thank you very much! this I smuch quicker than what I am being told to do
$endgroup$
– Niko
Feb 24 at 4:24
add a comment |
$begingroup$
Option:
Normal of the plane: $(1,1,1)$,
Normalized(i.e of unit length): $(1/√3)(1,1,1)$
Line through $(8,0,-6)$:
$vec r= (8,0,-6)+t (1/√3)(1,1,1)$.
Determine $t$ when line intersects plane:
$(8+t/√3)+t/√3+(-6+t/√3)=6;$
$3(t/√3)=4$;
$t= 4/√3.$
Distance = $4/√3$ (Why?).
$endgroup$
$begingroup$
Very nice application of vector algebra (+1). The answer could be improved by explicitly citing that the coefficients of the variables in the plane equations are the component of a vector orthogonal to the plane. And also answering the last "why?" could improve it. The OP (or other people reading the answer) might not be aware of this application of vector algebra. This answer would need a nice drawing to be great!
$endgroup$
– Lorenzo Donati
Feb 24 at 11:37
$begingroup$
Lorenzo.Thanks.If you feel any edits would be in place, feel free. This answer is an option, a bit of a different approach ,not just calculating a root, etc.Thank you again for your kind words.Greetings, Peter
$endgroup$
– Peter Szilas
Feb 24 at 13:31
add a comment |
$begingroup$
Option:
Normal of the plane: $(1,1,1)$,
Normalized(i.e of unit length): $(1/√3)(1,1,1)$
Line through $(8,0,-6)$:
$vec r= (8,0,-6)+t (1/√3)(1,1,1)$.
Determine $t$ when line intersects plane:
$(8+t/√3)+t/√3+(-6+t/√3)=6;$
$3(t/√3)=4$;
$t= 4/√3.$
Distance = $4/√3$ (Why?).
$endgroup$
$begingroup$
Very nice application of vector algebra (+1). The answer could be improved by explicitly citing that the coefficients of the variables in the plane equations are the component of a vector orthogonal to the plane. And also answering the last "why?" could improve it. The OP (or other people reading the answer) might not be aware of this application of vector algebra. This answer would need a nice drawing to be great!
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– Lorenzo Donati
Feb 24 at 11:37
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Lorenzo.Thanks.If you feel any edits would be in place, feel free. This answer is an option, a bit of a different approach ,not just calculating a root, etc.Thank you again for your kind words.Greetings, Peter
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– Peter Szilas
Feb 24 at 13:31
add a comment |
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Option:
Normal of the plane: $(1,1,1)$,
Normalized(i.e of unit length): $(1/√3)(1,1,1)$
Line through $(8,0,-6)$:
$vec r= (8,0,-6)+t (1/√3)(1,1,1)$.
Determine $t$ when line intersects plane:
$(8+t/√3)+t/√3+(-6+t/√3)=6;$
$3(t/√3)=4$;
$t= 4/√3.$
Distance = $4/√3$ (Why?).
$endgroup$
Option:
Normal of the plane: $(1,1,1)$,
Normalized(i.e of unit length): $(1/√3)(1,1,1)$
Line through $(8,0,-6)$:
$vec r= (8,0,-6)+t (1/√3)(1,1,1)$.
Determine $t$ when line intersects plane:
$(8+t/√3)+t/√3+(-6+t/√3)=6;$
$3(t/√3)=4$;
$t= 4/√3.$
Distance = $4/√3$ (Why?).
answered Feb 24 at 7:15
Peter SzilasPeter Szilas
11.6k2822
11.6k2822
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Very nice application of vector algebra (+1). The answer could be improved by explicitly citing that the coefficients of the variables in the plane equations are the component of a vector orthogonal to the plane. And also answering the last "why?" could improve it. The OP (or other people reading the answer) might not be aware of this application of vector algebra. This answer would need a nice drawing to be great!
$endgroup$
– Lorenzo Donati
Feb 24 at 11:37
$begingroup$
Lorenzo.Thanks.If you feel any edits would be in place, feel free. This answer is an option, a bit of a different approach ,not just calculating a root, etc.Thank you again for your kind words.Greetings, Peter
$endgroup$
– Peter Szilas
Feb 24 at 13:31
add a comment |
$begingroup$
Very nice application of vector algebra (+1). The answer could be improved by explicitly citing that the coefficients of the variables in the plane equations are the component of a vector orthogonal to the plane. And also answering the last "why?" could improve it. The OP (or other people reading the answer) might not be aware of this application of vector algebra. This answer would need a nice drawing to be great!
$endgroup$
– Lorenzo Donati
Feb 24 at 11:37
$begingroup$
Lorenzo.Thanks.If you feel any edits would be in place, feel free. This answer is an option, a bit of a different approach ,not just calculating a root, etc.Thank you again for your kind words.Greetings, Peter
$endgroup$
– Peter Szilas
Feb 24 at 13:31
$begingroup$
Very nice application of vector algebra (+1). The answer could be improved by explicitly citing that the coefficients of the variables in the plane equations are the component of a vector orthogonal to the plane. And also answering the last "why?" could improve it. The OP (or other people reading the answer) might not be aware of this application of vector algebra. This answer would need a nice drawing to be great!
$endgroup$
– Lorenzo Donati
Feb 24 at 11:37
$begingroup$
Very nice application of vector algebra (+1). The answer could be improved by explicitly citing that the coefficients of the variables in the plane equations are the component of a vector orthogonal to the plane. And also answering the last "why?" could improve it. The OP (or other people reading the answer) might not be aware of this application of vector algebra. This answer would need a nice drawing to be great!
$endgroup$
– Lorenzo Donati
Feb 24 at 11:37
$begingroup$
Lorenzo.Thanks.If you feel any edits would be in place, feel free. This answer is an option, a bit of a different approach ,not just calculating a root, etc.Thank you again for your kind words.Greetings, Peter
$endgroup$
– Peter Szilas
Feb 24 at 13:31
$begingroup$
Lorenzo.Thanks.If you feel any edits would be in place, feel free. This answer is an option, a bit of a different approach ,not just calculating a root, etc.Thank you again for your kind words.Greetings, Peter
$endgroup$
– Peter Szilas
Feb 24 at 13:31
add a comment |
$begingroup$
You can draw a line from your point to the plane and then find the length of its projection onto the unit normal vector to the plane.
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add a comment |
$begingroup$
You can draw a line from your point to the plane and then find the length of its projection onto the unit normal vector to the plane.
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add a comment |
$begingroup$
You can draw a line from your point to the plane and then find the length of its projection onto the unit normal vector to the plane.
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You can draw a line from your point to the plane and then find the length of its projection onto the unit normal vector to the plane.
answered Feb 24 at 4:46
BootsBoots
19810
19810
add a comment |
add a comment |
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$begingroup$
How did the $6$ become the $12$?
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– Theo Bendit
Feb 24 at 4:21
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because z = - x - y + 6. So since I plug in (z + 6)^2 in the distance formula, it becomes (-x - y + 12)^2
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– Niko
Feb 24 at 4:25