​ If vectors a and b are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA. ​

Question

If \(\vec a\) and \(\vec b\) are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.

Answer 1

We have been given that,

We need to find the position vector of C, that is, \(\vec {OC}\).

Also, we have

Substituting equation (ii) and (iii) in equation (i), we get