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Find the length and direction (when defined) of u x v and v x u, where u = 4i and v = -4j?

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Final answer:

The length and direction of the cross product of two vectors, u and v, can be found using the magnitude and angle between them. For the given vectors, u = 4i and v = -4j, the magnitude of the cross product is 16 and its direction is perpendicular to the plane formed by the original vectors.

Step-by-step explanation:

The length and direction of the cross product of two vectors, u and v, can be found using the formula u x v = |u||v|sinθ, where |u| and |v| are the magnitudes of the vectors and θ is the angle between them.

Given that u = 4i and v = -4j, the magnitude of the cross product can be calculated as |u x v| = |4||-4|sin90° = 16.

Since the cross product of two vectors in two dimensions is a vector perpendicular to the plane formed by the original vectors, the direction of u x v would be along the positive k-direction (out of the plane).

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