# Collinear vectors

I couldn't solve this problem guys:

Let vectors x, y, z be non zero vectors, no two of which are collinear. Find their sum if x+y is collinear with z and if y+z is collinear with x.

Also, what does a collinear vector mean?

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Hurkyl
Staff Emeritus
Gold Member
Two vectors are collinear if they lie along the same line.

The easiest algebraic description of collinearity is that two vectors v and w are collinear if and only if one is a scalar multiple of the other. That is, there exists a number &alpha; such that:

v = &alpha; w
or
w = &alpha; v

Two vectors are collinear if they lie along the same line.

The easiest algebraic description of collinearity is that two vectors v and w are collinear if and only if one is a scalar multiple of the other. That is, there exists a number &alpha; such that:

v = &alpha; w
or
w = &alpha; v
To be specific, vectors are collinear when their lines of action are parallel to each other.