Question

a and b are non-collinear vectors. If p = (2x + 1) a - band q = (x - 2)a +b are collinear vectors, then x = ______.

Options

• \[\frac{1}{3}\]

• - \[\frac{1}{3}\]

• -3

• 3

Answer 1

a and b are non-collinear vectors. If p = (2x + 1) a - band q = (x - 2)a +b are collinear vectors, then x = \[\underline{\frac{1}{3}}\].

Explanation:

Given, a and bare non-collinear vector and p =(2x + 1)a - b and q = (x - 2)a + b are collinear vector.

`therefore ((2x + 1)/(x - 2)) = (- 1)/1`

⇒ 2x + 1 = - x + 2

⇒ 3x = 1

⇒ x = `1/3`