Question

If \( \theta \) is the angle between two vectors \( \vec{a} \) and \( \vec{b} \) such that \( |\vec{a}| = 7 \), \( |\vec{b}| = 1 \) and \( |\vec{a} \times \vec{b}|^2 = k^2 - (\vec{a} \cdot \vec{b})^2 \), then the values of \( k \) and \( \theta \) are:

• A. \( k=1, \theta=45^\circ \)
• B. \( k=7, \theta=60^\circ \)
• C. \( k=49, \theta=90^\circ \)
• D. \( k=7 \) and \( \theta \) is arbitrary

Hint:

Whenever an angle \( \theta \) disappears from the final simplified equation, it means \( \theta \) is arbitrary and not uniquely determined by the given conditions.