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. $90^{∘}$
• B. $0^{∘}$
• C. $30^{∘}$
• D. $60^{∘}$

Answer 1

Answer: (B)

Given, $P=2\hat{i}−3\hat{j}+\hat{k}$,
$Q=−4\hat{i}+6\hat{j}−2\hat{k}$
$∴P×Q=â\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& −3& 1\\ −4& 6& −2\end{array}â$
$∴PQ\sin θ=\hat{i}(6−6)−\hat{j}(−4+4)+\hat{k}(12−12)$
$(âˆ\mu P×Q=PQ\sin θ)$
$⇒PQ\sin θ=0$
$\sin θ=0$
$θ=0^{∘}$