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If $\theta$ is the angle between $\mathbf{a}$ and $\mathbf{b}$ and $|\mathbf{a} \times \mathbf{b}|=|\mathbf{a} \cdot \mathbf{b}|$, then $\theta$ is equal to
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Verified Answer
The correct answer is:
$\frac{\pi}{4}$
Given that,
$|\mathbf{a} \times \mathbf{b}|=\mid \mathbf{a} \cdot \mathbf{b}$
$\begin{aligned} \Rightarrow & & |\mathbf{a}||\mathbf{b}||\sin \theta| & =|\mathbf{a}||\mathbf{b}||\cos \theta| \\ & \Rightarrow & \tan \theta & =1 \\ & \Rightarrow & \theta & =\frac{\pi}{4}\end{aligned}$
$|\mathbf{a} \times \mathbf{b}|=\mid \mathbf{a} \cdot \mathbf{b}$
$\begin{aligned} \Rightarrow & & |\mathbf{a}||\mathbf{b}||\sin \theta| & =|\mathbf{a}||\mathbf{b}||\cos \theta| \\ & \Rightarrow & \tan \theta & =1 \\ & \Rightarrow & \theta & =\frac{\pi}{4}\end{aligned}$
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