Question

Which of the following property is incorrect?

• A. $\hat{a}.\hat{b}$ = $\hat{b}.\hat{a}$
• B. $\hat{a}.(\hat{b}+\hat{c})=\hat{a}.\hat{b}+\hat{a}.\hat{c}$
• C. $\hat{i}.\hat{j}=\hat{j}.\hat{k}=\hat{k}.\hat{i}=1$
• D. $\hat{i}.\hat{i}=\hat{j}.\hat{j}=\hat{k}.\hat{k}=1$

Answer 1

The correct option is C $\hat{i}.\hat{j}=\hat{j}.\hat{k}=\hat{k}.\hat{i}=1$

$\hat{a}.\hat{b}=|\hat{a}||\hat{b}|\cos \theta$
$\hat{i}$ and $\hat{j}$ make angle $\theta ={90}^{\circ }$ , so $\cos \theta =0$
$\therefore \hat{i}.\hat{j}=0$

similarly,
$\hat{j}.\hat{k}=\hat{k}.\hat{i}=\hat{i}.\hat{j}=0$