How to find the equation of a plane with two vectors only...

Question

anonymous · Answer

cross them , get a normal vector

anonymous · Answer

then ?? I dont know any point lying in that plane...

anonymous · Answer

The the vectors must be linearly independent, and they should start at some given point,  If U and V are the vectors and they start at P(u, v, w), then we can compute the normal vector to the plane by taking the cross product of U and V.  Let N be that normal vector, and point Q(x, y, z) be a point on the plane.  Then 
N dot (Q - P) = 0 will be the equation of the plane.

anonymous · Answer

The vector equation of a plane is n ⋅ (r − r0) = 0, where n is a vector that is normal to the plane and r, r0 are position vectors in the plane (in other words they are defined with reference to an origin). The normal vector n is given by the cross.