Question

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

• A. u and v have the same direction
• B. u and v are perpendicular
• C. u and v have the opposite direction
• D. Data Insufficient

Answer 1

Answer: (B)

$|u+v|=|u-v|$
Squaring on both sides,
$|u+v{|}^2=|u-v{|}^2$
$|u{|}^2+|v{|}^2+2\bar{u}v=|u{|}^2+|v{|}^2+2(\bar{u}v)$
$4\bar{u},\bar{v})=0$
$\bar{u}\cdot v=0$
$\bar{u}\perp \bar{v}$