Mathematics - Vector Question with Solution | TestHub

$\begin{array}{rl}& \vec{a}\times (\hat{i}+\hat{j})=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 1& -1\\ 1& 1& 0\end{array}\right|\\ & =\hat{i}-\hat{j}+\hat{k}\\ & (\vec{a}\times (\hat{i}\times \hat{j}))\times \hat{i}=\hat{k}+\hat{j}\\ & ((\vec{a}\times (\hat{i}\times \hat{j}))\times i)\times \hat{i}=\hat{j}-\hat{k}\\ & \mathrm{projection}\text{ of }\vec{a}\text{ on }\hat{b}=\frac{\vec{a}\cdot \vec{b}}{|\vec{b}|}\\ & =\frac{1+1}{\sqrt{2}}=\sqrt{2}\end{array}$