Question

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

Options

• `(3vec"a" + 2vec"b")/3`

• `vec"a"`

• `(5vec"a" - vec"b")/3`

• `(4vec"a" + vec"b")/3`

Answer 1

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

Explanation:

Applying section formula the position vector of the required point is

`(2(vec"a" + vec"b") + 1(2vec"a" - vec"b"))/(2 + 1) = (4vec"a" + vec"b")/3`