Question

Show that `vec A*vec B=(1)/(4) |vec A+vec B|^(2)-|vec A-vec B|^(2)​

Answer 1

Explanation:

Given ∣a∣=1,∣∣∣∣b∣∣∣∣=4a.b=2 and c=(2a×b)−3b

a.b=2⇒∣a∣∣b∣.cos(a,b)=2

1×4×cosθ=2

cosθ=21⇒θ=60∘ (Angle b/w a,b)

a×b=∣a∣∣b∣.sinθ=1×4×sin60=4×22=23

Given c=2a