cross product

Question

The cross product î × ĵ equals

RankGuru · Accepted Answer

1. **Cyclic Rule**: For Right-Handed Coordinate Systems:
   - $\hat{i} 	imes \hat{j} = \hat{k}$
   - $\hat{j} 	imes \hat{k} = \hat{i}$
   - $\hat{k} 	imes \hat{i} = \hat{j}$
2. **Anti-cyclical**: Reversing the order flips the sign (e.g., $\hat{j} 	imes \hat{i} = -\hat{k}$).
3. **Geometry**: The unit vector $\hat{k}$ is perpendicular to the $xy$-plane containing $\hat{i}$ and $\hat{j}$.

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