Mathematics - Vector Question with Solution | TestHub

$(\hat{i}\times \vec{a}\cdot \vec{b})\hat{i}+(\hat{j}\times \vec{a}\cdot \vec{b})\hat{j}+(\hat{k}\times \vec{a}\cdot \vec{b})\hat{k}$ $=(\hat{i}\cdot \vec{a}\times \vec{b})\hat{i}+(\hat{j}\cdot \vec{a}\times \vec{b})\hat{j}+(\hat{k}\cdot \vec{a}\times \vec{b})\hat{k}$ $(\because \vec{a}\times \vec{b}\cdot \vec{c}=\vec{a}\cdot \vec{b}\times \vec{c})$ $=(\vec{a}\times \vec{b})\hat{i}+(\vec{a}\times \vec{b})\hat{j}+(\vec{a}\times \vec{b})\hat{k}$ $==\vec{a}\times \vec{b}$