Let $|\vec a|= 5,|\vec b|=2$ and $\vec a.\vec b= 6$, then the value of $|\vec a×\vec b|$ is equal to
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 8
Use the identity:
$|\vec a\times \vec b|^{2}=|\vec a|^{2}\,|\vec b|^{2}-(\vec a\cdot \vec b)^{2}$
Given:
$|\vec a|=5,\;|\vec b|=2,\;\vec a\cdot \vec b=6$
$|\vec a\times \vec b|^{2} =5^{2}\cdot 2^{2}-6^{2} =25\cdot 4-36 =100-36 =64$
$|\vec a\times \vec b|=\sqrt{64}=8$
The value of $|\vec a\times \vec b|$ is $8$.