Question

Two vectors having magnitude such that second vector is half of the first vector and resultant vector is 20% greater than first vector they are incline to each other by theta . calculate angle theta

Answer 1

If the magnitude of the resultant of two equal vectors is equal to that of either vector, find the angle between them.

My Attempt: Let a⃗ a→ and b⃗ b→ be two vectors such that ∥a⃗ ∥=∥b⃗ ∥‖a→‖=‖b→‖

Magnitude of Resultant:

=a2+b2+2abcosθ−−−−−−−−−−−−−−√=a2+b2+2abcos⁡θ

=2a2+2abcosθ−−−−−−−−−−−−√