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
