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Questions  >>  CBSE XII  >>  Math  >>  Vector Algebra
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Q)

If $\theta$ is the angle between any two vectors $\overrightarrow {a} $ and $\overrightarrow {b}$ , then $|\overrightarrow {a} . \overrightarrow {b} | = |\overrightarrow {a} \times \overrightarrow {b}|$, then what is the value of $\theta$


$(A)\; \frac{\pi}{2}$
$(B)\; \frac{\pi}{4}$
$(C)\; 0$
$(D)\; \frac{\pi}{3}$

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A)
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$|\overrightarrow {a} . \overrightarrow {b}| = |a| |b| \cos \theta $
$|\overrightarrow {a} \times \overrightarrow {b}| = |a| | b| \sin \theta$
Given : $|\overrightarrow {a} . \overrightarrow {b}| = | \overrightarrow{a} \times \overrightarrow {b}|$
$\implies |a| |b| \cos \theta = |a| |b| \sin \theta $
$\tan \theta = 1$
$\therefore \theta = \frac{\pi}{4}$
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