Question

Find the cross product of the unit vectors: \[ \hat{k} \times \hat{j} \]

• A. \( -\hat{i} \)
• B. \( \hat{j} \)
• C. 0
• D. \( \hat{k} \)

Hint:

The cross product of unit vectors follows the cyclic order \( \hat{i} \to \hat{j} \to \hat{k} \) and changes sign when the order is reversed. Use the right-hand rule to determine the direction.

Answer 1

The Correct Option is A

The cross product of two unit vectors follows the right-hand rule and is based on the cyclic relationship of the unit vectors \( \hat{i}, \hat{j}, \hat{k} \). The cyclic cross product rules are: \[ \hat{i} \times \hat{j} = \hat{k}, \quad \hat{j} \times \hat{k} = \hat{i}, \quad \hat{k} \times \hat{i} = \hat{j} \] For \( \hat{k} \times \hat{j} \), we follow the right-hand rule and find: \[ \hat{k} \times \hat{j} = -\hat{i} \] Thus, the correct answer is: \[ \boxed{-\hat{i}} \]