<(u x v), u> is greater than 0 for all vectors u and v in R^3.
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.© BrainMass Inc. brainmass.com October 10, 2019, 2:23 am ad1c9bdddf
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: ...
This solution thoroughly demonstrates the equation of a plane.