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If $(\mathbf{a} \times \mathbf{b})^2+(\mathbf{a} \cdot \mathbf{b})^2=144$ and $|\mathbf{a}|=4$, then $|\mathbf{b}|=$
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The correct answer is:
3
We know that $(\mathbf{a} \times \mathbf{b})^2+(\mathbf{a} \cdot \mathbf{b})^2=|\mathbf{a}|^2|\mathbf{b}|^2$ $\therefore 144=16|\mathbf{b}|^2 \Rightarrow|\mathbf{b}|=3$.
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