Mathematics - Vector Question with Solution | TestHub

Dotting the given relation with $\hat{b}$ gives $\hat{a}\cdot \hat{b}=0$, and dotting it with $\hat{a}$ gives $\hat{a}\cdot \vec{c}=1$. Therefore $\hat{a},\hat{b}$ are perpendicular and $\vec{c}=\hat{a}\times \hat{b}+\hat{a}$. Thus $[\hat{a}\hat{b}\vec{c}]=(\hat{a}\times \hat{b})\cdot \vec{c}=1$.