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1. Vector eqn of a line - what way?
If I have a vector equation of a line eg

Then I can see the direction is (1,1) ie at 45 degree angle. And I can easily visualise this line in my mind.

If there were a point A and a point B on the line then the vector AB would be different to the vector BA. Is there a concept of the way line is going - the sort of arrow of the line? Or is it just seen as a line which goes in both directions into infinity and there is no concept of 'what way'? Just wondering?
2. Re: Vector eqn of a line - what way?
You can consider the direction as lambda increases or as lambda decreases if you like.
3. Re: Vector eqn of a line - what way?
(Original post by BabyMaths)
You can consider the direction as lambda increases or as lambda decreases if you like.
Not quite sure I understand. Are you suggesting positive lambda is one way, -ve the other?
4. Re: Vector eqn of a line - what way?
(Original post by acomber)
Not quite sure I understand. Are you suggesting positive lambda is one way, -ve the other?
Not positive and negative but rather, increasing and decreasing.
5. Re: Vector eqn of a line - what way?
(Original post by acomber)
If I have a vector equation of a line eg

Then I can see the direction is (1,1) ie at 45 degree angle. And I can easily visualise this line in my mind.

If there were a point A and a point B on the line then the vector AB would be different to the vector BA. Is there a concept of the way line is going - the sort of arrow of the line? Or is it just seen as a line which goes in both directions into infinity and there is no concept of 'what way'? Just wondering?
The displacement vector you give certainly has a direction, namely a combination of 1 unit in the positive x direction and one unit in the positive y direction. However the line itself has no sense of direction...it simply depends on whether the lambda is positive or negative to give a particular point on the line. So if the lambda is positive then you are going to travel from the given point on the line in the same direction as the displacement vector and if lambda is negative then you are going to travel in the opposite direction to that given by the displacement vector. So...the displacement vector has a direction and the line is just a line extending to infinity in either direction.