Question

Two vectors $P$ and $Q$ are given in space as $P =2 \hat{ i }-3 \hat{ j }+\hat{ k }$ and $Q =-4 \hat{ i }+6 \hat{ j }-2 \hat{ k }$. The angle between $P$ and $Q$ is

• A. $90^{\circ}$
• B. $0^{\circ}$
• C. $30^{\circ}$
• D. $60^{\circ}$

Answer 1

Answer: (B)

Given, $P =2 \hat{ i }-3 \hat{ j }+\hat{ k }$,
$Q =-4 \hat{ i }+6 \hat{ j }-2 \hat{ k }$
$\therefore P \times Q =\begin{vmatrix}\hat{ i } & \hat{ j } & \hat{ k } \\ 2 & -3 & 1 \\ -4 & 6 & -2\end{vmatrix}$
$\therefore P Q \sin \theta=\hat{ i }(6-6)-\hat{ j }(-4+4)+\hat{ k }(12-12)$
$(\because P \times Q =P Q \sin \theta)$
$\Rightarrow P Q \sin \theta=0$
$\sin \theta=0$
$\theta=0^{\circ}$