let u be a nonzero vector in space and let v and w be any two vectors in space. if u.v = u.w and u x v = u x w, can you conclude that v=w? give reason for your answer.

my answer ::

v is not necessary equal to w

since u is nonzero vector thus the cross product of the vector u with v and w will produce another vector and it is consider the same if theirsmagnitude and directionsare same while their dot product will produce a scalar which has no indication of direction. thus v and w is not necessary same vector.

is my argument is true... or can anyone improve it and prove it with example... your help is highly appreciated.... thanx