Question

TWO VECTORS, EACH OF MAGNITUDE 'A' COMBINES TO GIVE RESULTANT OF MAGNITUDE 'A' . THEN FIND THE ANGLE BETWEEN TWO VECTORS AND THE ANGLE OF RESULTANT.

Answer 1

The magnitude of resultant of two vectors P and Q is given by,

R = √[P² + Q² + 2PQ cos θ]

According to the question, P = Q = R = A. Then,

A = √[A² + A² + 2A² cos θ]

A² = 2A² + 2A² cos θ

A² + 2A² cos θ = 0

A²(1 + 2 cos θ) = 0

Since A ≠ 0,

1 + 2 cos θ = 0

cos θ = - 1 / 2

=> θ = 120°

Hence angle between the two vectors is 120°.

The angle of resultant of two vectors P and Q is given by,

tan α = Q sin θ / (P + Q cos θ)

Hence here,

tan α = A sin 120° / (A + A cos 120°)

tan α = sin 120° / (1 + cos 120°)

tan α = (√3 / 2) / (1 - (1 / 2))

tan α = (√3 / 2) / (1 / 2)

tan α = √3

=> α = 60°

Hence angle of resultant is 60°.