Question

Find the position vector of a point R which divides the line joining the two points P and Q with position vectors `vec"OP" = 2vec"a" + vec"b"` and `vec"OQ" = vec"a" - 2vec"b"`, respectively, in the ratio 1:2 internally

Answer 1

The position vector of the point R dividing the join of P and Q internally in the ratio 1:2 is given by

`vec"OR" = (2(2vec"a" + vec"b") + 1(vec"a" - 2vec"b"))/(1 + 2)`

= `(5vec"a")/3`.