If \( |\vec{a}|=5\ ,\ |\vec{b}|=6 \) and \( \vec{a}.\vec{b}=18 \) , then value of \( |\vec{a}\times\vec{b}| \) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 24
By the identity \( |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2=|\vec{a}|^2|\vec{b}|^2 \) (Lagrange’s identity):
\( |\vec{a}\times\vec{b}|^2=25\times 36-18^2 \)
\( =900-324 \)
\( =576 \)
\( |\vec{a}\times\vec{b}|=24 \)