Question

Find the vector product of the vectors \(\vec{a}=-\hat{j}+\hat{k}\) and \(\vec{b}=-\hat{i}-\hat{j}-\hat{k}\).

(a) \(2\hat{i}-\hat{j}+\hat{k}\)

(b) \(2\hat{i}-\hat{j}-4\hat{k}\)

(c) \(\hat{i}+\hat{j}-\hat{k}\)

(d) \(2\hat{i}-\hat{j}-\hat{k}\)

The question was asked in examination.

Query is from Product of Two Vectors-2 in division Vector Algebra of Mathematics – Class 12

Answer 1

The correct choice is (d) \(2\hat{i}-\hat{j}-\hat{k}\)

To elaborate: Given that, \(\vec{a}=-\hat{j}+\hat{k}\) and \(\vec{b}=-\hat{i}-\hat{j}-\hat{k}\)

Calculating the vector product, we get

\(\vec{a}×\vec{b}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\0&-1&1\\-1&-1&-1\end{vmatrix}\)

=\(\hat{i}(1-(-1))-\hat{j}(0-(-1))+\hat{k}(0-1)\)

=\(2\hat{i}-\hat{j}-\hat{k}\)