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 $

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If $\sin \theta + \cos \theta = 1$, then $\sin \theta \cos \theta = $
If $A$ and $B$ are any two sets, then $A \cap (A \cup B)$ is equal to
Let $m, n \in N$ and $\operatorname{gcd}(2, n)=1$. If $30\left(\begin{array}{l}30 \\ 0\end{array}\right)+29\left(\begin{array}{l}30 \\ 1\end{array}\right)+\ldots+2\left(\begin{array}{l}30 \\ 28\end{array}\right)+1\left(\begin{array}{l}30 \\ 29\end{array}\right)= n .2^{ m }$ then $n + m$ is equal to $($Here $\left.\left(\begin{array}{l} n \\ k \end{array}\right)={ }^{ n } C _{ k }\right)$
Differential equation whose solution is $y = cx + c - {c^3}$, is
If  $A$  and  $B $ be symmetric matrices of the same order, then $AB - BA$ will be a
$A (2,6,2), B (-4,0, \lambda), C (2,3,-1)$ and $D (4,5,0)$, $|\lambda| \leq 5$ are the vertices of a quadrilateral $A B C D$. If its area is $18$ square units, then $5-6 \lambda$ is equal to $.........$.
If $\tan \left(\frac{\pi}{9}\right), x, \tan \left(\frac{7 \pi}{18}\right)$ are in arithmetic progression and $\tan \left(\frac{\pi}{9}\right), y, \tan \left(\frac{5 \pi}{18}\right)$ are also in arithmetic progression, then $|x-2 y|$ is equal to:
The probability that a teacher will give an unannounced test during any class meeting is $1/5$. If a student is absent twice, then the probability that the student will miss at least one test is
The figure in the complex plane given by $10 z \bar{z}-3\left(z^2+z^{-2}\right)+4 i\left(z^2-z^{-2}\right)=0$ is