Question

The values of \(\lambda\) such that \((x,y,z) \ne (0,0,0)\) and \[ (\hat{i} + \hat{j} + 3\hat{k})x + (3\hat{i} - 3\hat{j} + \hat{k})y + (-4\hat{i} + 5\hat{j})z = \lambda(x\hat{i} + y\hat{j} + z\hat{k}) \]

• A. \(0,1\)
• B. \(-1,1\)
• C. \(-1,0\)
• D. \(-2,0\)

Hint:

For vector equations of form \(A\vec{X}=\lambda \vec{X}\), directly form matrix and solve determinant.

Answer 1

The Correct Option is C