Find the vector product of the vectors \(\vec{a}=2\hat{i}+4\hat{j}\) and \(\vec{b}=3\hat{i}-\hat{j}+2\hat{k}\).

(a) \(\hat{i}-19\hat{j}-4\hat{k}\)

(b) \(3\hat{i}+19\hat{j}-14\hat{k}\)

(c) \(3\hat{i}-19\hat{j}-14\hat{k}\)

(d) \(3\hat{i}+5\hat{j}+4\hat{k}\)

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The origin of the question is Product of Two Vectors-2 in chapter Vector Algebra of Mathematics – Class 12

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Right option is (c) 3\hat{i}-19\hat{j}-14\hat{k}

The explanation: Given that, \vec{a}=2\hat{i}+4\hat{j} and \vec{b}=3\hat{i}-\hat{j}+2\hat{k}

Calculating the vector product, we get

\vec{a}×\vec{b}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\2&4&-5\\3&-1&2\end{vmatrix}

=\hat{i}(8-5)-\hat{j}(4-(-15))+\hat{k}(-2-12)

=3\hat{i}-19\hat{j}-14\hat{k}