Question

two vector equal in magnitude have resultant equal to magnitude of either.find angle between them
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Answer 1

angle b/w resultant and one vector ( \alpha ) = theta / 2

Answer 2

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

Resultant of two equal vector is equal to magnitude of either.

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

We have to find angle between them.

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

➠ Let two vectors A and B are inclined at an angle θ and resultant of them be R.

ATQ, |A| = |B| = |R| ➝ x

➠ By triangle law or parallelogram law of vector addition, the magnitude of resultant R at two vectors A and B inclined to each other at angle θ, is given by

$\dag\:\boxed{\bf{\red{R=\sqrt{A^2+B^2+2AB\cos\theta}}}}$

Let's calculate :D

$:\implies\tt\:R=\sqrt{A^2+B^2+2AB\cos\theta}$

$:\implies\tt\:x^2=x^2+x^2+2(x)(x)\cos\theta$

$:\implies\tt\:x^2-2x^2=2x^2\cos\theta$

$:\implies\tt\:\cos\theta=\dfrac{-x^2}{2x^2}=-\dfrac{1}{2}$

$:\implies\tt\:\theta=\cos^{-1}-\dfrac{1}{2}$

$:\implies\boxed{\bf{\gray{\theta=120^{\circ}}}}$