Question

If \( \mathbf{a} = \mathbf{c} \) and \( \mathbf{b} = \mathbf{a} \times \mathbf{c} \), then the correct statement is:

• A. \( \mathbf{a} \parallel (\mathbf{b} - \mathbf{c}) \)
• B. \( \mathbf{a} = 0 \) or \( \mathbf{b} = \mathbf{c} \)
• C. \( \mathbf{a} = \mathbf{b} \)
• D. None of these

Hint:

The cross product of two vectors is zero if and only if the vectors are parallel.

Answer 1

The Correct Option is B

Step 1: Analyze the given vector relations.
Given that \( \mathbf{a} = \mathbf{c} \) and \( \mathbf{b} = \mathbf{a} \times \mathbf{c} \), we know that the cross product of two parallel vectors is zero. Hence, \( \mathbf{a} = 0 \) or \( \mathbf{b} = \mathbf{c} \).
Thus, the correct answer is (2).