If \(|\vec{a}\times \vec{b}|^2+|\vec{a}\cdot \vec{b}|^{2}=144\) and \(|\vec{a}|=4\), then \(|\vec{b}|\) is equal to

\(12\) \(8\) \(4\) \(3\)

\(3\)

\(\begin{aligned}|\vec{a}\times \vec{b}|^2+|\vec{a}\cdot \vec{b}|^2&=|a|^2|b|^2\\ 144&=16\cdot |\vec{b}|^{2}\\ |\vec{b}|^{2}&=9\\ |\vec{b}|&=3\end{aligned}\)