# Thread: Prove that the vector is collinear

1. ## Prove that the vector is collinear

Referred to the origin O, A and B are two points which have position vectors a and b respectively. Prove that the point P whose position vector p is given by p = λa + (1-λ)b is collinear with A and B.

2. ## Re: Prove that the vector is collinear

Originally Posted by alexander9408
Referred to the origin O, A and B are two points which have position vectors a and b respectively. Prove that the point P whose position vector p is given by p = λa + (1-λ)b is collinear with A and B.
$a-p &=a-\lambda a (1-\lambda)b = (1-\lambda) a (1-\lambda)b =(1-\lambda) (a - b)$
Because $(a-p)$ is a multiple of $(a-b)$ then $a,~b,~\&~p$ are collinear.

3. ## Re: Prove that the vector is collinear

Sorry, I still don't get it, why when (a-p) is the multiple of (a-b) then a,b, p are collinear?

4. ## Re: Prove that the vector is collinear

Originally Posted by alexander9408
Sorry, I still don't get it, why when (a-p) is the multiple of (a-b) then a,b, p are collinear?
The kind of help that you need is beyond this forum.
You need to sit down with a live tutor.

5. ## Re: Prove that the vector is collinear

Originally Posted by alexander9408
Sorry, I still don't get it, why when (a-p) is the multiple of (a-b) then a,b, p are collinear?
Do you understand what "collinear means"? Saying that P is "collinear" with A and B means that it lies on the line throught A and B.
That means that the vector from A to B and the vector from A to P have the sam direction and so one is a multiple of the other.

6. ## Re: Prove that the vector is collinear

Yeah, finally I'm able to figure it out how it work. Anyways, thank you guys.

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### collinear prof in vector

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