If is the angle between any two vectors a and b, then | a. b | = … - Vidyadip

Question

If $\theta $ is the angle between any two vectors $\vec a$ and $\vec b$, then $\left| {\vec a.\vec b} \right| = \left| {\vec a \times \vec b} \right|$ when θ is equal to

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Answer

We have:
$|\vec a.\vec b|=|\vec a \times \vec b|$
$\Rightarrow |\vec a||\vec b|cos\theta =|\vec a||\vec b|sin\theta$
$\Rightarrow cos\theta=\sin\theta$
$\Rightarrow tan\theta =1\Rightarrow \theta=\frac{\pi}{4}$

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