Question

Write the value of $\left(\hat{i}\times \hat{j}\right)·\hat{k}+\left(\hat{j}+\hat{k}\right)·\hat{j}$

Answer 1

$$\begin{gathered} \left(\hat{i}\times \hat{j}\right).\hat{k}+\left(\hat{j}+\hat{k}\right).\hat{j} \\ =\hat{k}.\hat{k}+\hat{j}.\hat{j}+\hat{k}.\hat{j}(\because \hat{i}\times \hat{j}=\hat{k}) \\ ={\left|\hat{k}\right|}^2+{\widehat{\left|j\right|}}^2+0(\because \hat{k}.\hat{j}=0) \\ =1^2+1^2 \\ =2 \end{gathered}$$