# Prove that the vector is collinear

• Aug 16th 2012, 10:51 PM
alexander9408
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.

• Aug 17th 2012, 03:29 AM
Plato
Re: Prove that the vector is collinear
Quote:

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.
• Aug 17th 2012, 06:16 AM
alexander9408
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?
• Aug 17th 2012, 06:32 AM
Plato
Re: Prove that the vector is collinear
Quote:

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.
• Aug 17th 2012, 06:38 AM
HallsofIvy
Re: Prove that the vector is collinear
Quote:

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.
• Aug 17th 2012, 06:53 AM
alexander9408
Re: Prove that the vector is collinear
Yeah, finally I'm able to figure it out how it work. Anyways, thank you guys.