If u v and w are vectors in a real inner pmduct space V and

If u, v, and w are vectors in a real inner pmduct space V, and if k is a scalar, then: (0, v) = (v. 0) = 0 (u, v + w) = {u, v) + (u, w) {u, v - W) = (u, v) - (u, w)

Solution

a) <0 , v> = <v, 0> =0

Let vector v = xi +yj

0 = oi +0j

inner product<0, v> = (0i +0j)(xi +yj) = 0*x +0*j = 0

inner product<v, 0> = (xi +yj)(0i +0j) = x*0 +y*0 = 0

Hence proved