Question

If \( \mathbf{a} = 2i - 2j + k \) and \( \mathbf{c} = -i + 2k \), then \( \mathbf{a} \times \mathbf{c} \) is equal to:

• A. \( 2\sqrt{5} \mathbf{i} + 5 \mathbf{j} + \sqrt{5} \mathbf{k} \)
• B. \( 2\mathbf{i} - 2\mathbf{j} + \sqrt{5} \mathbf{k} \)
• C. \( 5 \mathbf{i} + \sqrt{5} \mathbf{j} + 2\mathbf{k} \)
• D. \( \sqrt{5} \mathbf{i} + 2 \mathbf{j} + \mathbf{k} \)

Hint:

To calculate the cross product, use the determinant method with unit vectors \( \mathbf{i}, \mathbf{j}, \mathbf{k} \) in the first row.

Answer 1

The Correct Option is B

Using the cross-product formula, \[ \mathbf{a} \times \mathbf{c} = \begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 2 & -2 & 1 \\ -1 & 0 & 2 \end{vmatrix} \] we get the result \( 2\mathbf{i} - 2\mathbf{j} + \sqrt{5} \mathbf{k} \).