Question

If \( \theta \) is the angle between two vectors \( \vec{a} \) and \( \vec{b} \) such that \( |\vec{a}| = 7, |\vec{b}| = 1 \) and \[ |\vec{a} \times \vec{b}|^2 = k^2 - (\vec{a} - \vec{b})^2, \] 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 \( \theta \) arbitrary

Hint:

For mixed vector identities: \begin{itemize} \item Use dot and cross magnitude formulas. \item Substitute option angles to simplify. \end{itemize}

Answer 1

The Correct Option is B