If p and q are unequal unit vectors such that ( p - q ) . ( ( 2 q… - Vidyadip

MCQ

If $\vec p$ and $\vec q$ are unequal unit vectors such that $\left( {\vec p - \vec q} \right) . \left( {\left( {2\vec q + \vec p} \right) \times \left( {3\vec p - \vec q} \right)} \right) = \left| {\vec p + \vec q} \right|$ , then angle between $\vec p$ and $\vec q$ will be

A
$\frac{\pi }{2}$
B
$\frac{\pi }{4}$
✓
$\pi $
D
$0$

✓

Answer

Correct option: C.

$\pi $

c
$\overrightarrow{\mathrm{p}}-\overrightarrow{\mathrm{q}}, 2 \overrightarrow{\mathrm{q}}+\overrightarrow{\mathrm{p}}$ and $3 \overrightarrow{\mathrm{p}}-\overrightarrow{\mathrm{q}}$ are coplanar

$L.H.S. = 0 \Rightarrow {\rm{R}}.{\rm{H}}.{\rm{S}}. = 0 \Rightarrow \overrightarrow {\rm{p}} = - \overrightarrow q $

$\overrightarrow {\rm{p}} \wedge \overrightarrow q = \pi $

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