Question

The value of \(\{(\vec{a} \times \vec{b})^2 + (\vec{a}\cdot \vec{b})^2\\div a^2 b^2\) is}

• A. 0
• B. 1
• C. 2
• D. None of these

Hint:

Always remember: \(|\vec{a}\times\vec{b}|^2 + (\vec{a}\cdot\vec{b})^2 = a^2 b^2\).

Answer 1

The Correct Option is B

Concept: Vector identity: \(|\vec{a}\times\vec{b}|^2 + (\vec{a}\cdot\vec{b})^2 = a^2 b^2\).

Step 1: Substitute. \[ \frac{a^2 b^2}{a^2 b^2} = 1 \]