Question

The resultant of two vectors A and B is perpendicular to vector A and its magnitude is equal to half of the magnitude of vector B. Then the angle between A and B is

Options

• 30°

• 45°

• 150°

• 120°

Answer 1

Given:

The resultant of `vecA` & `vecB` is perpendicular to `vecA` and the magnitude of the resultant (C) = `1/2 vecB` and α = 90°

Solution:

(i) Magnitude of resultant:

`C^2 = A^2 + B^2 + 2AB costheta`

`B^2/4 = A^2 + B^2 + 2AB(A/B)`

`-3/4B^2 = 3A^2 ⇒ B^2 = 4A^2` i.e. B = 2A

(ii) direction of resultant:

tan α = `(B sintheta)/(A + B costheta)`

∞ = `(Bsintheta)/(A + B costheta)`

A + B cos θ = 0

cos θ = `-"A"/"B" = -"A"/(2"A") = -1/2`

cos θ = `-1/2`

θ = `cos^-1(-1/2)`

θ = 120°