Let $|\vec a|= 5,|\vec b|=2$ and $\vec a.\vec b= 6$, then the value of $|\vec a×\vec b|$ is equal to

8

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 $8$.