Question

The position vector of the point which divides the join of points `2vec"a" - 3vec"b"` and `vec"a" + vec"b"` in the ratio 3:1 is ______.

Options

• `(3vec"a" - 2vec"b")/2`

• `(7vec"a" - 8vec"b")/4`

• `(3vec"a")/4`

• `(5vec"a")/4`

Answer 1

The position vector of the point which divides the join of points `2vec"a" - 3vec"b"` and `vec"a" + vec"b"` in the ratio 3:1 is `(5vec"a")/4`.

Explanation:

The given vectors are  `2vec"a" - 3vec"b"` and `vec"a" + vec"b"` in the ratio 3:1.

∴ The position vector of the required point c which divides the join of the given vectors `vec"a"` and `vec"b"` is

`vec"c" = ("m"_1x_2 + "m"_2x_1)/("m"_1 + "m"_2)`

= `(1 * (2vec"a" - 3vec"b") + 3(vec"a" + vec"b))/(3 + 1)`

= `(2vec"a" - 3vec"b" + 3vec"a" + 3vec"b")/4`

= `(5vec"a")/4`

= `5/4 vec"a"`