Question
If $\mathbf{a} \cdot \mathbf{b}=\sqrt{3}$ and $\mathbf{a} \times \mathbf{b}=\langle 1,2,2\rangle,$ find the angle between a and $\mathbf{b} .$
Step 1
Given that $\mathbf{a} \cdot \mathbf{b} = \sqrt{3}$, we can write this as $\sqrt{3} = |\mathbf{a}| |\mathbf{b}| \cos \theta$. Therefore, $\cos \theta = \frac{\sqrt{3}}{|\mathbf{a}| |\mathbf{b}|}$. Show more…
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