Calculus III: The Cross Product (Level 1 of 9)

The video introduces the cross product, a vector operation distinct from scalar multiplication and the dot product. It is defined only for vectors in three-dimensional space (R cubed). The cross product results in a vector perpendicular to the plane containing the original vectors, with a magnitude based on the sine of the angle between them. The direction is determined using the right-hand rule, and the operation is non-commutative. The video also compares the cross product with the dot product, highlighting their differences in output and applicable dimensions.

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