Question

In a clockwise system

• A. $\hat{j}\times \hat{k}=\hat{i}$
• B. $\hat{i}.\hat{i}=0$
• C. $\hat{j}\times \hat{j}=1$
• D. $\hat{k}.\hat{j}=1$

Answer 1

The correct option is A

$\hat{j}\times \hat{k}=\hat{i}$

Explanation for correct option:

Here as we know , $\hat{i}$, $\hat{j}$ and $\hat{k}$ are the unit vectors.

Option A : $\hat{j}\times \hat{k}=\hat{i}$

Since the system is clockwise, the cross product of $\hat{k}$ and $\hat{j}$ is $\hat{i}$ as they both are perpendicular to each other.

Option B : $\hat{i}.\hat{i}=0$

Now $\hat{i}$ and $\hat{i}$ are in the same direction, therefore their dot product will be $1$.

Option C : $\hat{j}\times \hat{j}=1$

The cross product of $\hat{j}$ and $\hat{j}$ should be zero as both the vectors are in a similar direction.

Option D : $\hat{k}.\hat{j}=1$

The dot product of $\hat{k}$ and $\hat{i}$ will be zero as both are in the opposite direction

Hence, the correct option is A.