Difference in finding the direction of a line in 2D and 3D using perpendiculars
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What i'm trying to do is understand the differences between lines in 2D and 3D, and could use some clarification.
The textbook i'm using states that:
"In two dimensions the direction of a line is determined either by a vector along the line or by a vector perpendicular to it.
In three dimensions the situation is different: the direction of a line is determined uniquely by a vector perpendicular (normal) to it; the direction of a plane is determined uniquely by a vector perpendicular (normal) to it, but there are many different pairs of vectors parallel to the plane which can be used to describe it"
My question is:
In that first sentence the books specifically said "by a vector along the
line". But wouldn't i be able to get the direction of a line if i got the
vector of a second line that is parallel and in the same direction as
the first one?In the second sentence about the bit on the 3D line, why is it "uniquely"
determined by only the normal? Why cant i solve it like 2D lines and use
vectors along the line or maybe use a second line that's in the same
direction and parallel to it to find for the direction of the first line?
vector-spaces
asked Nov 20 at 4:44
Usama Abdul
82
add a comment |
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0
down vote
favorite
What i'm trying to do is understand the differences between lines in 2D and 3D, and could use some clarification.
The textbook i'm using states that:
"In two dimensions the direction of a line is determined either by a vector along the line or by a vector perpendicular to it.
In three dimensions the situation is different: the direction of a line is determined uniquely by a vector perpendicular (normal) to it; the direction of a plane is determined uniquely by a vector perpendicular (normal) to it, but there are many different pairs of vectors parallel to the plane which can be used to describe it"
My question is:
In that first sentence the books specifically said "by a vector along the
line". But wouldn't i be able to get the direction of a line if i got the
vector of a second line that is parallel and in the same direction as
the first one?In the second sentence about the bit on the 3D line, why is it "uniquely"
determined by only the normal? Why cant i solve it like 2D lines and use
vectors along the line or maybe use a second line that's in the same
direction and parallel to it to find for the direction of the first line?
vector-spaces
asked Nov 20 at 4:44
Usama Abdul
82
In three dimensions the direction of a line is uniquely determined by a vector parallel to it, not perpendicular.
– amd
Nov 21 at 1:15
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
What i'm trying to do is understand the differences between lines in 2D and 3D, and could use some clarification.
The textbook i'm using states that:
"In two dimensions the direction of a line is determined either by a vector along the line or by a vector perpendicular to it.
In three dimensions the situation is different: the direction of a line is determined uniquely by a vector perpendicular (normal) to it; the direction of a plane is determined uniquely by a vector perpendicular (normal) to it, but there are many different pairs of vectors parallel to the plane which can be used to describe it"
My question is:
In that first sentence the books specifically said "by a vector along the
line". But wouldn't i be able to get the direction of a line if i got the
vector of a second line that is parallel and in the same direction as
the first one?In the second sentence about the bit on the 3D line, why is it "uniquely"
determined by only the normal? Why cant i solve it like 2D lines and use
vectors along the line or maybe use a second line that's in the same
direction and parallel to it to find for the direction of the first line?
vector-spaces
asked Nov 20 at 4:44
Usama Abdul
82
What i'm trying to do is understand the differences between lines in 2D and 3D, and could use some clarification.
The textbook i'm using states that:
"In two dimensions the direction of a line is determined either by a vector along the line or by a vector perpendicular to it.
In three dimensions the situation is different: the direction of a line is determined uniquely by a vector perpendicular (normal) to it; the direction of a plane is determined uniquely by a vector perpendicular (normal) to it, but there are many different pairs of vectors parallel to the plane which can be used to describe it"
My question is:
In that first sentence the books specifically said "by a vector along the
line". But wouldn't i be able to get the direction of a line if i got the
vector of a second line that is parallel and in the same direction as
the first one?In the second sentence about the bit on the 3D line, why is it "uniquely"
determined by only the normal? Why cant i solve it like 2D lines and use
vectors along the line or maybe use a second line that's in the same
direction and parallel to it to find for the direction of the first line?
vector-spaces
vector-spaces
asked Nov 20 at 4:44
Usama Abdul
82
asked Nov 20 at 4:44
Usama Abdul
82
asked Nov 20 at 4:44
Usama Abdul
82
asked Nov 20 at 4:44
Usama Abdul
82
asked Nov 20 at 4:44
Usama Abdul
82
82
In three dimensions the direction of a line is uniquely determined by a vector parallel to it, not perpendicular.
– amd
Nov 21 at 1:15
add a comment |
In three dimensions the direction of a line is uniquely determined by a vector parallel to it, not perpendicular.
– amd
Nov 21 at 1:15
In three dimensions the direction of a line is uniquely determined by a vector parallel to it, not perpendicular.
– amd
Nov 21 at 1:15
In three dimensions the direction of a line is uniquely determined by a vector parallel to it, not perpendicular.
– amd
Nov 21 at 1:15
add a comment |
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In three dimensions the direction of a line is uniquely determined by a vector parallel to it, not perpendicular.
– amd
Nov 21 at 1:15