# Q19  Choose the correct. If  $\theta$ is the angle between any two vectors  $\vec a \: \:and \: \: \vec b$ , then  $|\vec a \cdot \vec b |=|\vec a \times \vec b |$ when $\theta$ is equal to $\\A ) 0 \\\\ B ) \pi /4 \\\\ C ) \pi / 2 \\\\ D ) \pi$

Given in the question

$\theta$ is the angle between any two vectors  $\vec a \: \:and \: \: \vec b$ and $|\vec a \cdot \vec b |=|\vec a \times \vec b |$

To find the value of $\theta$

$|\vec a \cdot \vec b |=|\vec a \times \vec b |$

$|\vec a|| \vec b |cos\theta=|\vec a|| \vec b |sin\theta$

$cos\theta=sin\theta$

$tan\theta =1$

$\theta =\frac{\pi}{4}$

Hence option D is correct.

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