# The equation of a plane

Part I:

<(u x v), u> is greater than 0 for all vectors u and v in R^3.

Part II:

The equation of the plane through the origin determined by two vectors u and v in R^3 is <(u x v), x> = 0.

Are these statements true or false and please explain why.

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#### Solution Preview

I. The statement is false. The cross-product u x v is perpendicular to both u and v, and so the dot product of (u x v) and u is zero for all u and v from R^3.

II. This statement is true. The equation of a plane can be derived as follows: ...

#### Solution Summary

This solution thoroughly demonstrates the equation of a plane.

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