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

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 150°.

Explanation:

`B/2 = sqrt(A^2 + B^2 + 2AB costheta)`     ...(i)

∴ tan 90° = `(B sin theta)/(A + B cos theta)`

⇒ A + B cos  = 0

∴ `cos theta = -A/B`

Hence, from (i) `B^2/A`

= A² + B² − 2A²

⇒ A = `sqrt3B/2`

⇒ cos θ = `-A/B`

= `-sqrt3/2`

θ = 150°