Question

Let \( \mathbf{a} = \hat{i} - \hat{k}, \mathbf{b} = x\hat{i} + \hat{j} + (1 - x)\hat{k}, \mathbf{c} = y\hat{i} + x\hat{j} + (1 + x - y)\hat{k} \). Then, \( [\mathbf{a} \, \mathbf{b} \, \mathbf{c}] \) depends on:}

• A. only \( y \)
• B. only \( x \)
• C. both \( x \) and \( y \)
• D. neither \( x \) nor \( y \)

Hint:

When working with scalar triple products, simplify the determinant step by step and carefully analyze the dependence on variables.