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Math Help - Prove that the vector is collinear

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    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.

    Please show your answer in detail, I really can’t understand about this one. Thank you.
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    Re: Prove that the vector is collinear

    Quote Originally Posted by alexander9408 View Post
    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.
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    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?
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    Re: Prove that the vector is collinear

    Quote Originally Posted by alexander9408 View Post
    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.
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    Re: Prove that the vector is collinear

    Quote Originally Posted by alexander9408 View Post
    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.
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    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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