Question

If \(A (\bar{a}) \) and \( B(\bar{b}) \) be any two vectors of the points \( A \) and \( B \) and \( r \) be the position vector of point \( R \) divides the line \( A B \) internally in the ratio \( m : n \), then prove that \( r=\frac{m \bar{b}+n \bar{a}}{m+n} \)

Answer 1

R is a point on the line segment AB(A – R – B) and \(\overline{AR} \,and\, \overline{RB}\) are in the same direction.

Point R divides AB internally in the ratio m : n