If \(|\vec{a}| = 10\), \(|\vec{b}| = 2\) and \(\vec{a} \cdot \vec{b} = 12\), then value of \(|\vec{a} \times \vec{b}|\) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 16
Since \(\vec{a} \cdot \vec{b} = |\vec{a}||\vec{b}|\cos\theta\) and \(|\vec{a} \times \vec{b}| = |\vec{a}||\vec{b}|\sin\theta\), adding their squares gives Lagrange’s identity:
\(|\vec{a} \times \vec{b}|^2 + (\vec{a} \cdot \vec{b})^2 = |\vec{a}|^2|\vec{b}|^2\)
\(|\vec{a} \times \vec{b}|^2 = 100 \times 4 - 144 = 256\)
\(|\vec{a} \times \vec{b}| = 16\)
NCERT Exemplar:
Vector Algebra
