Question

\((3\vec{k}-7\vec{i})\times 2\vec{k}=\) ?

• A. \(-14\vec{j}\)
• B. \(14\vec{j}\)
• C. \(11\vec{i}-2\vec{k}\)
• D. \(2\vec{k}-11\vec{i}\)

Hint:

Only the terms with nonzero minors survive; watch the sign in the middle cofactor.

Answer 1

The Correct Option is B

Write components: \((3\vec{k}-7\vec{i})=(-7,0,3)\), \(2\vec{k}=(0,0,2)\). Use determinant for cross product: \[ \begin{vmatrix} \vec{i}&\vec{j}&\vec{k} \\ [-2pt] -7&0&3 \\ 0&0&2 \end{vmatrix} = \vec{i}(0\cdot2-3\cdot0)\ -\ \vec{j}(-7\cdot2-3\cdot0)\ +\ \vec{k}(-7\cdot0-0\cdot0) = 14\vec{j}. \]