Question

The position vector of the points A and B are a and b respectively. IfP divides AB internally in the ratio 3 : 1 and Q is the midpoint of AP,then find position vector of Q.

Answer 1

Therefore the coordinate of Q is   $\frac{5a+3b}{8}$

Step-by-step explanation:

Given that the position vector of A is a and B is b.

And P is divides AB internally in the ratio 3:1

∴  The coordinate of P is $\frac{1.a+3.b}{3+1} = \frac{a+3b}{4}$

∵Q is midpoint of AB .

So the coordinate of Q is $\frac{\frac{a+3b}{4}+a }{2}=\frac{5a+3b}{8}$