Question

Find the position vector of the point which divides the join of points with position vectors `vec"a" + 3vec"b" and vec"a"- vec"b"` internally in the ratio 1 : 3. 

Answer 1

Required position vector is `(1(vec"a" - vec"b") + 3(vec"a" + 3vec"b"))/(1 + 3)`

= `(1(vec"a" - vec"b") + 3(vec"a" + 3vec"b"))/(4)`

= `vec"a" + 2vec"b"`.