Mathematics - Vector Question with Solution | TestHub

$\begin{array}{rl}& \overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{a}}\times (\hat{\mathrm{i}}-3\hat{\mathrm{k}})\\ & =\left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ 3& -1& 2\\ 1& 0& -2\end{array}\right|=2\hat{\mathrm{i}}+8\hat{\mathrm{j}}+\hat{\mathrm{k}}\\ & \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}}\times \hat{\mathrm{k}}=8\hat{\mathrm{i}}-2\hat{\mathrm{j}}\\ & \overrightarrow{\mathrm{c}}-2\hat{\mathrm{j}}=8\hat{\mathrm{i}}-4\hat{\mathrm{j}}\end{array}$ Projection of $(\hat{\mathrm{i}}-2\hat{\mathrm{j}})$ on $\overrightarrow{\mathrm{a}}$ $\begin{array}{rl}& (\overrightarrow{\mathrm{c}}-2\hat{\mathrm{j}})\cdot \hat{\mathrm{a}}=\frac{⟨8,-4,0⟩\cdot ⟨3,-1,2⟩}{\sqrt{14}}\\ & =\frac{28}{\sqrt{14}}=2\sqrt{14}\end{array}$