If `| vec axx vec b|=4,\ | vec adot vec b|=2,\ t h e n\ | vec a|^2| vec b|^2=` `6` b. `2` c. `20` d. 8

Explanation

`|\vec{a} \times \vec{b}|=4 \quad\text{and} \quad|\vec{a} \cdot \vec{b}|=2-1`

Squaing and adding,

`|\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2} &=4^{2}+2^{2} `

`|a|^{2}|b|^{2} \sin ^{2} \theta+|a|^{2}|b|^{2} \cos ^{2} \theta =16+4 `

`|a|^{2}|b|^{2}[\sin ^{2} \theta+\cos ^{2} \theta]=20 `

`\Rightarrow \quad|\vec{a}|^{2}|\vec{b}|^{2}+20`