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** = λ**a** + (1-λ)**b** is collinear with A and B.

Please show your answer in detail, I really can’t understand about this one. Thank you.

Re: Prove that the vector is collinear

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**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** = λ**a** + (1-λ)**b** is collinear with A and B.

$\displaystyle a-p &=a-\lambda a –(1-\lambda)b = (1-\lambda) a –(1-\lambda)b =(1-\lambda) (a - b)$

Because $\displaystyle (a-p)$ is a multiple of $\displaystyle (a-b)$ then $\displaystyle a,~b,~\&~p$ are collinear.

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?

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.

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.

Re: Prove that the vector is collinear

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