Question

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

Answer 1

$$\begin{gathered} \hat{i}.\left(\hat{j}\times \hat{k}\right)+\hat{j}.\left(\hat{k}\times \hat{i}\right)+\hat{k}.\left(\hat{i}\times \hat{j}\right) \\ =\hat{i}.\hat{i}+\hat{j}.j+\hat{k}.\hat{k} \\ ={\left|\hat{i}\right|}^2+{\left|\hat{j}\right|}^2+{\left|\hat{k}\right|}^2 \\ =1+1+1 \\ =3 \end{gathered}$$