If \( |\vec{a}|=2,|\vec{b}|=7,\vec{a}\times\vec{b}=3\hat{\imath}+2\hat{\jmath}+6\hat{k} \) , then the angle between \( \vec{a} \) and \( \vec{b} \) is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{\pi}{6} \)
\( |\vec{a}\times\vec{b}|=\sqrt{9+4+36}=7 \)
Using \( |\vec{a}\times\vec{b}|=|\vec{a}|\,|\vec{b}|\sin\theta \):
\( 7=2\times 7\times\sin\theta \)
\( \displaystyle \sin\theta=\frac{1}{2} \)
\( \displaystyle \theta=\frac{\pi}{6} \)