Question

if a = 3i+5j and b = 6i+9j are the position vectors of A and B, find the position vector of C, which divides AB internally in the ratio 2:5(m:n​

Answer 1

Given :

a = 3i + 5j ; b = 6i + 9j

Vector c which divides AB internally in the ratio 2 : 5

⇒ m : n = 2 : 5

Formula :

The position vector C dividing another vector AB in the ratio m : n internally is given by ,

              $c = \frac{mb \ +\ na}{m \ + \ n}$

Solution :

⇒ $c = \frac{2(6i+9j) \ +\ 5(3i + 5j)}{2 \ + \ 5}$

⇒ $c = \frac{(12i + 18j) \ +\ (15i+25j)}{7}$

⇒ $c = \frac{27i + 43j}{7}$

 ∴ c = (27/7)i + (43/7)j