Find Sum of Collinear Vectors x, y, z

[PiRsq]

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?

 

[Hurkyl]

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 α such that:

v = α w
or
w = α v

 

[CHUKKY]

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 α such that:

v = α w
or
w = α v

To be specific, vectors are collinear when their lines of action are parallel to each other.