If | a|=2, | b|=5, | a b|=8, then a b is:

Question

If $|\vec a|=2$, $|\vec b|=5$, $|\vec a	imes\vec b|=8$, then $\vec a\cdot\vec b$ is:

Accepted Answer

$$|\vec a\times\vec b|^2+(\vec a\cdot\vec b)^2 = |\vec a|^2|\vec b|^2 \implies 64+(\vec a\cdot\vec b)^2=100 \implies (\vec a\cdot\vec b)^2=36 \implies \vec a\cdot\vec b=6$$

Solutions · 1