If the position vector of a point A is a +2 b and a divides A B in the ratio 2: 3 , then the position vector of B is

Step-by-step solution

Let the position vector of point A be r _A = a + 2 b . Let the position vector of point B be r _B . The point with position vector a divides the line segment AB in the ratio 2:3 . Using the section formula, the position vector of the point dividing AB in ratio m:n is m r _B + n r _A m+n . Here, m=2 , n=3 , and the point is a . Thus, a = 2 r _B + 3( a + 2 b ) 2+3 a = 2 r _B + 3 a + 6 b 5 5 a = 2 r _B + 3 a + 6 b 2 r _B = 5 a - 3 a - 6 b 2 r _B = 2 a - 6 b r _B = a - 3 b Answer: a -3 b