Let $u$ and $v$ be two non zero vectors, if $|u+v|=|u-v|$, then

Question

Aicharya · Accepted Answer

$|\mathrm{u}+\mathrm{v}|=|\mathrm{u}-\mathrm{v}|$ Squaring on both sides, $\begin{aligned} |\mathrm{u}+\mathrm{v}|^2 & =|\mathrm{u}-\mathrm{v}|^2 \ |\mathrm{u}|^2+|\mathrm{v}|^2+\overline{\bar{u} v} & =|\mathrm{u}|^2+|\mathrm{v}|^2+2(\bar{u} v) \ 4(\bar{u} \cdot \bar{v}) & =0 \ \bar{u}, v & =0 \ \bar{u} & \perp \bar{v} \end{aligned}$ Hence, option (b) is correct.

Let \(u\) and \(v\) be two non zero vectors, if \(|u+v|=|u-v|\), then

Solution