Question

For non-zero & non-collinear vectors $p$ and $q$, the value of $\left[\hat{i}pq\right]\hat{i}+\left[\hat{j}pq\right]\hat{j}+\left[\hat{k}pq\right]\hat{k}$ is

• A. $0$
• B. $2(p\times q)$
• C. $(q\times p)$
• D. $(p\times q)$

Answer 1

Answer: (D)

$(p\times q)$

$\begin{array}{c}\left(\hat{i}pq\right)\hat{i}+\left(\hat{j}pq\right)\hat{j}+\left(\hat{k}pq\right)\hat{k}\\ =\left(\left(p\times q\right)\hat{i}\right)\hat{i}+\left(\left(p\times q\right)\hat{j}\right)\hat{j}+\left(\left(p\times q\right)\hat{k}\right)\hat{k}\\ ={\left(p\times q\right)}_1\hat{i}+{\left(p\times q\right)}_2\hat{j}+{\left(p\times q\right)}_3\hat{k}\\ =\left(p\times q\right)\\ Hence,\\ optionDiscorrectanswer.\end{array}$