Question

If \( \vec{a} \) is a non-zero vector then \( |\vec{a} \times \vec{a}| \) is equal to:

• A. \( |\vec{a}| \)
• B. \( |\vec{a}|^2 \)
• C. 1
• D. 0

Hint:

For any vector \( \vec{a} \), \( \vec{a} \times \vec{a} = \vec{0} \), and its magnitude will always be 0.

Answer 1

The Correct Option is D

Step 1: Understanding the Cross Product.
The cross product of any vector with itself is always 0. Therefore, \[ \vec{a} \times \vec{a} = \vec{0} \] Step 2: Taking the Magnitude.
The magnitude of the zero vector is always zero. Thus, \[ |\vec{a} \times \vec{a}| = |\vec{0}| = 0 \] Step 3: Conclusion.
Hence, the correct answer is \( 0 \), corresponding to option (D).