Question

If \( \vec{a} = \hat{i} + 4\hat{j} - 4\hat{k}, \ \vec{b} = -2\hat{i} + 5\hat{j} - 2\hat{k} \), and \( \vec{c} = 3\hat{i} - 2\hat{j} - 4\hat{k} \) are three vectors such that \( (\vec{b} \times \vec{c}) \times \vec{a} = x\hat{i} + y\hat{j} + z\hat{k} \), then \( x + y - z = \)

• A. \( 75 \)
• B. \( -89 \)
• C. \( 125 \)
• D. \( -389 \)

Hint:

Use determinant expansion to compute cross products. The vector triple product identity can also simplify nested cross products if needed.

Answer 1

The Correct Option is A