Question

The resultant of two equal forces is equal to their magnitude

Answer 1

If A⃗ ,B⃗ A→,B→ are the two equal vectors and R⃗ R→ is their resultant

we have,

R⃗ =A⃗ +B⃗ R→=A→+B→

if∥A⃗ ∥=∥B⃗ ∥=∥C⃗ ∥=Lif‖A→‖=‖B→‖=‖C→‖=L

then,

∥R⃗ ∥2=∥A⃗ ∥2+∥B⃗ ∥2−2∥A⃗ ∥∥B⃗ ∥cos(θ)‖R→‖2=‖A→‖2+‖B→‖2−2‖A→‖‖B→‖cos⁡(θ)

L2=2L2−2L2cos(θ)L2=2L2−2L2cos⁡(θ)

⇒θ=cos−1(12)