Question

For any vector \( \vec{p} \), the value of \( 2\left[|\vec{p}\times \hat{i}|^2 + |\vec{p}\times \hat{j}|^2 + |\vec{p}\times \hat{k}|^2\right] \) is

• A. \( 4|\vec{p}|^2 \)
• B. \( 2|\vec{p}|^2 \)
• C. \( 4|\vec{p}| \)
• D. \( 2|\vec{p}| \)

Hint:

Use \( |\vec{a}\times\vec{b}|^2 = |\vec{a}|^2|\vec{b}|^2 - (\vec{a}\cdot\vec{b})^2 \) or component method for unit vectors.

Answer 1

The Correct Option is A