Question

a and b are non-collinear vectors. If c = (x - 2)a + b and d = (2x + 1)a - b are collinear vectors, then the value of x = ______.

विकल्प

• `1/2`

• `1/4`

• `1/5`

• `1/3`

Answer 1

a and b are non-collinear vectors. If c = (x - 2)a + b and d = (2x + 1)a - b are collinear vectors, then the value of x = `underline(1/3)`.

Explanation:

Given, c = (x - 2)a + b and

d = (2x + 1)a - b are collinear

∴ c = λd

⇒ (x - 2)a + b = λ[(2x + 1)a - b]

⇒ `(x - 2)/(2x + 1) = 1/(- 1) = lambda`

⇒ 2x + 1 = - x + 2

⇒ 3x = 1

⇒ x = `1/3`