If \(\left|\vec{a}\times \vec{b}\right|^{2}+\left|\vec{a}\cdot \vec{b}\right|^{2}=144\) and \(\left|\vec{a}\right|=4\) then \(\left|\vec{b}\right|\) is equal to
Answer & explanation
Correct answer: option 4
\(\begin{aligned}\left|\vec{a}\times \vec{b}\right|^{2}+\left|\vec{a}\cdot \vec{b}\right|^{2}&=\left|a\right|^{2}\left|b\right|^{2}\\ 144&=16|\vec{b}|^{2}\\ |\vec{b}|^{2}&=9\\ |\vec{b}|&=3\end{aligned}\)