Question

Compute the following cross products. Then make a sketch showing the two vectors and their cross product. j×k- \mathbf { j } \times \mathbf { k }

Solution

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The magnitude of a cross product of vectors u\mathbf u and v\mathbf v is defined as

u×v=uvsin(u,v)|\mathbf u \times \mathbf v|=|\mathbf u| |\mathbf v| \sin \angle (\mathbf u, \mathbf v)

The vector u×v\mathbf u \times \mathbf v is orthogonal to both vectors u\mathbf u and v\mathbf v. Its direction is determined by the right-hand rule, which means, when putting u\mathbf u and v\mathbf v to start at the same point and let the fingers of a right hand to curl from u\mathbf u to v\mathbf v, the thumb points to the direction of a cross product u×v\mathbf u \times \mathbf v.

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