V R3 u barv bar u1 v1 2u2 v2 u3 v3 B SolutionvR3uvu1v

V = R^3, (u bar|v bar) = u_1 v_1 + 2u_2 v_2 + u_3 v_3 B = {, , }

Solution

v=R^3,{u,v}=u1v1+2u2v2+u3v3 this is the vector process.

hre u.v=u1v1+u2v2=u3v3

product of the sets.

here we can take u=(2,1,1) v=(-1,2,-2)

u1.v1=2.-1=-2

u2.v2=1.2=2

u3.v3=1.-2=-2

now calculate u1v1+2u2v2+u3v3

=-2+2(2)+(-2)

=0