Question

If a➝ and b➝ are two unit vectors such that a➝ + b➝
and a➝ - 2b➝ are perpendicular then the angle
between a➝ and b➝ is
(a) ???? (b) ????
4 3
(c) ???? (d)????
6

Answer 1

Given: a and b are unit vectors, i.e., |a| = 1, |b| = 1

Also given that, (a + b) and (a - 2 b) are perpendicular to each other. Then

(a + b) . (a - 2 b) = 0

or, a . a - 2 a . b + a . b - 2 b . b = 0

or, a² - a . b - 2 b² = 0

or, |a|² - a . b - 2 |b|² = 0, since a² = |a|²

or, 1² - a . b - 2 (1²) = 0

or, 1 - a . b - 2 = 0

or, a . b = - 1

or, |a| |b| cosθ = cos(180°)

or, cosθ = cos(180°)

or, θ = 180°

∴ the angle between the vectors a and b is 180° .