Question

If $|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|$ then $|\overrightarrow{a}\times \overrightarrow{b}|$=_____ if $|\overrightarrow{a}|=3$,$|\overrightarrow{b}|=1$

Answer 1

If $|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|$, then $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular to each other.
$|\overrightarrow{a}\times \overrightarrow{b}|=|\overrightarrow{a}||\overrightarrow{b}|\sin \theta$
Here, $\theta =\pi /2$
$\therefore |\overrightarrow{a}\times \overrightarrow{b}|=3$