# Explain under what conditions, the resultant of two vectors will be equal to either of them.

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Explain under what conditions, the resultant of two vectors will be equal to either of them.

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The resultant of two vectors will be equal to either of them if :

(i) The two vectors will be equal to either of them if :

(ii) The two vectors are inclined to each other at an angle of 120º.

Explanation – Let X be magnitude of each of the two vectors say $\vec P$ and $\vec Q$ . if θ = angle between $\vec P$ and $\vec Q$ , then the magnitude of their resultant vector ($\vec R$ ) is given by the relation

R = $\sqrt{P^2+Q^2+2PQ\,cos\,\theta}$

= $\sqrt{X^2+X^2+2X^2\,cos\,120^o}$

$\sqrt{2X^2[1+cos(90^o+30^o)]}$

= $\sqrt{2X^2[1-sin\,30^o]}$

= $\sqrt{2X^2(1-\frac{1}{2})}$   (∴ sin 30º = $\frac{1}{2}$)

= $\frac{2X^2}{2}$ = X