Mathematics - Vector Question with Solution | TestHub

According to question $\mathrm{a}=-\hat{i}+\hat{j}+\hat{k}$ and $\mathrm{b}=\hat{i}-\hat{j}+\hat{k}$ Then, $\mathrm{a}\times \mathrm{b}=\left|\begin{array}{lll}\hat{i}& \hat{j}& \hat{k}\\ -1& 1& 1\\ 1& -1& 1\end{array}\right|$ $\begin{array}{c}=\hat{i}[1+1]-\hat{j}[-1-1]+\hat{k}[1-1]=2(\hat{i}+\hat{j})\\ \text{ and }|\mathrm{a}\times \mathrm{b}|=\sqrt{4+4}=2\sqrt{2}\end{array}$ $\therefore \text{ Required unit vector }=\pm \frac{2(\hat{i}+\hat{j})}{2\sqrt{2}}=\pm \frac{\hat{i}+\hat{j}}{\sqrt{2}}$