Write the value of `[ hat i+ hat j\ hat j+ hat k\ hat k+ hat i]`

Explanation

$$ \begin{aligned} &\text{On solving}\\ &{[(\hat{\imath}+\hat{\jmath}) \cdot(\hat{\imath}+\hat{k} \times \hat{k}+\hat{\imath})]} \\ &(\hat{\imath}+\hat{\imath})[\hat{\imath}-\hat{k}+0+\hat{\imath}]] \\ &(\hat{\imath}+\hat{\imath}) \cdot[\hat{\imath}-\hat{k}+\hat{\jmath})=1+1=2 . \end{aligned} $$