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