Question

\((10\vec{i}+\vec{j}+\vec{k})\times(-4\vec{i}+7\vec{j}-11\vec{k})=\) ?

• A. \(-18\vec{i}+106\vec{j}+74\vec{k}\)
• B. \(18\vec{i}-106\vec{j}-74\vec{k}\)
• C. \(18\vec{i}+106\vec{j}+74\vec{k}\)
• D. \(5\vec{i}-6\vec{j}-7\vec{k}\)

Hint:

Cofactor signs are \(+,-,+\) across the top row.

Answer 1

The Correct Option is A

Use determinant: \[ \begin{vmatrix} \vec{i}&\vec{j}&\vec{k} \\ 10&1&1 \\ -4&7&-11 \end{vmatrix} = \vec{i}(1\cdot(-11)-1\cdot 7)\ -\ \vec{j}(10\cdot(-11)-1\cdot(-4))\ +\ \vec{k}(10\cdot 7-1\cdot(-4)). \] Compute: \(\vec{i}(-11-7)-\vec{j}(-110+4)+\vec{k}(70+4)=-18\vec{i}+106\vec{j}+74\vec{k}\).