Question

Let \(\mathbf{a} = \mathbf{i} - \mathbf{k}, \quad \mathbf{b} = x\mathbf{i} + \mathbf{j} + (1-x)\mathbf{k}, \quad \mathbf{c} = y\mathbf{i} + x\mathbf{j} + (1+x-y)\mathbf{k}\). 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:

Check cancellation in determinants before concluding dependence.

Answer 1

The Correct Option is D