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

June 28, 2026

The resultant of two equal vectors is equal in magnitude to each of them when the angle between the vectors is 120∘120^\circ 120∘.

Key idea in simple words

Take two vectors A⃗\vec AA and B⃗\vec BB of the same magnitude AAA, with an angle θ\theta θ between them.

The magnitude of their resultant R⃗\vec RR is

R=A2+A2+2A2cos⁡θ=2A2(1+cos⁡θ).R=\sqrt{A^2+A^2+2A^2\cos\theta}=\sqrt{2A^2(1+\cos\theta)}.R=A2+A2+2A2cosθ=2A2(1+cosθ).

You want the resultant to be equal to either of the vectors, so set R=AR=AR=A.

A=2A2(1+cos⁡θ).A=\sqrt{2A^2(1+\cos\theta)}.A=2A2(1+cosθ).

Squaring both sides and simplifying (assuming A≠0A\neq 0A=0) gives

1=2(1+cos⁡θ)⇒1=2+2cos⁡θ⇒−1=2cos⁡θ⇒cos⁡θ=−12.1=2(1+\cos\theta)\Rightarrow 1=2+2\cos\theta \Rightarrow -1=2\cos\theta \Rightarrow \cos\theta =-\frac12.1=2(1+cosθ)⇒1=2+2cosθ⇒−1=2cosθ⇒cosθ=−21.

The angle whose cosine is −12-\tfrac12 −21 is 120∘120^\circ 120∘.

So, when the angle between two equal vectors is 120∘120^\circ 120∘, their resultant has the same magnitude as each vector.

Visual mini-story (to imagine it)

Picture two equal arrows starting from the same point.
Open them so that the angle between them is 120∘120^\circ 120∘.
If you now draw the diagonal of the parallelogram formed by these two arrows, that diagonal (the resultant) will have exactly the same length as each arrow.

So the condition is:

When two equal vectors have an angle of 12 0∘120^\circ 120∘ between them, the resultant is equal in magnitude to each of the vectors.

TL;DR: For two equal vectors, the resultant equals either one of them (in magnitude) only if the angle between them is 120∘120^\circ 120∘.

Information gathered from public forums or data available on the internet and portrayed here.