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 externally

Answer 1

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

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

= `3vec"a" + 4vec"b"`.