when will the resultant of two equal vectors be equal to each other explain

The resultant of two equal vectors will be equal to either of the vectors themselves when the angle between the two vectors is 120 degrees. Explanation:
Consider two vectors A⃗\vec{A}A and B⃗\vec{B}B with equal magnitude ppp. The magnitude of their resultant vector R⃗\vec{R}R is given by the formula:

R=A2+B2+2ABcos⁡θR=\sqrt{A^2+B^2+2AB\cos \theta}R=A2+B2+2ABcosθ​

Since A=B=pA=B=pA=B=p, substitute:

R=p2+p2+2p2cos⁡θ=2p2+2p2cos⁡θR=\sqrt{p^2+p^2+2p^2\cos \theta}=\sqrt{2p^2+2p^2\cos \theta}R=p2+p2+2p2cosθ​=2p2+2p2cosθ​

For the resultant to be equal to either vector's magnitude ppp:

p=2p2+2p2cos⁡θp=\sqrt{2p^2+2p^2\cos \theta}p=2p2+2p2cosθ​

Squaring both sides and simplifying:

p2=2p2+2p2cos⁡θ ⟹ 1=2+2cos⁡θ ⟹ 2cos⁡θ=−1 ⟹ cos⁡θ=−12p^2=2p^2+2p^2\cos \theta \implies 1=2+2\cos \theta \implies 2\cos \theta =-1\implies \cos \theta =-\frac{1}{2}p2=2p2+2p2cosθ⟹1=2+2cosθ⟹2cosθ=−1⟹cosθ=−21​

This corresponds to:

θ=120∘\theta =120^\circ θ=120∘

Therefore, the resultant of two vectors of equal magnitude is equal in magnitude to either of the vectors only when the angle between them is 120 degrees.