Question

Under what condition does the equality (a vector + b vector) equal to magnitude of | a vector minus b vector| hold good

Answer 1

|a-b|=|a+b|

when a perpendicular b

also when b=0 vector

Answer 2

seems , your question took a little mistake. it's good if you will add picture of your question.

well I think your question is ----> Under what condition does the equality $|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|$ hold good ?


we know, formula,
$|\vec{a}+\vec{b}|=\sqrt{a^2+b^2+2abcos\theta}$

$|\vec{a}-\vec{b}|=\sqrt{a^2+b^2-2abcos\theta}$

so, $\sqrt{a^2+b^2+2abcos\theta}=\sqrt{a^2+b^2-2abcos\theta}$

$2abcos\theta=-2abcos\theta$

$cos\theta=0$

$\theta=\frac{\pi}{2}$