# Let are the position vectors of three points A, B and C. There exists non-zero scalars x, y & z, such that and x + y + z = 0, then show that A, B and C are collinear.

### Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Here,_{} are the position vectors of three points A, B and C. There exists non-zero scalars x, y & z, such that_{}

_{}

Also, x + y + z = 0 or x + y = – z

_{}

This shows that the point C divides the line joining the points A and B in the ratio of y : x. Hence, A, B and C are collinear.

### Answered by | 4th Jun, 2014, 03:23: PM

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