Question

The value of \(|\vec{a} \times \vec{b} + \vec{b} \times \vec{a}|\) is

• A. 1
• B. \(2|\vec{a} \times \vec{b}|\)
• C. 0
• D. None of these

Hint:

\(\vec{a} \times \vec{b}\) and \(\vec{b} \times \vec{a}\) are equal in magnitude but opposite in direction.

Answer 1

The Correct Option is C

Concept: Cross product is anti-commutative: \(\vec{a} \times \vec{b} = -(\vec{b} \times \vec{a})\).

Step 1: Add the vectors. \[ \vec{a} \times \vec{b} + \vec{b} \times \vec{a} = \vec{a} \times \vec{b} - \vec{a} \times \vec{b} = 0 \]

Step 2: Take magnitude. \[ |0| = 0 \]