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- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.Let F = 2xi + 3yj and let C be a smooth closed loop in R enclosing a region with non-zero area. Show that F · nˆ cannot be zero at every point in C, where nˆ is the unit normal vector pointing out of C.
