Question

If $\hat{i},\hat{j},\hat{k}$are unit vectors, then
(a) $\hat{i}·\hat{j}=1$

(b) $\hat{i}·\hat{i}=1$

(c) $\hat{i}\times \hat{j}=1$

(d) $\hat{i}\times \left(\hat{j}\times \hat{k}\right)=1$

Answer 1

(b) $\hat{i}·\hat{i}=1$

$$\begin{gathered} \text{Let us check each option one by one.} \\ \left(\mathrm{a}\right)\text{We know} \\ \hat{i}.\hat{j}=0 \\ \ne 1 \\ \left(\mathrm{b}\right)\text{We know} \\ \hat{i}.\hat{i}={\left|\hat{i}\right|}^2 \\ =1^2 \\ =1 \\ \left(\mathrm{c}\right)\hat{i}\times \hat{j}=\hat{k} \\ \ne 1 \\ \left(\mathrm{d}\right)\hat{i}\times \left(\hat{j}\times \hat{k}\right)=\hat{i}\times \hat{i} \\ =0 \\ \ne 1 \end{gathered}$$