For p= ao+at+azz and q=bo+bi+b, the standard inner product in the vector space P, is defined by: = aobo + ab + ab. (a) Given p=1+2r+z and q=2-x+2r. Evaluate the following: (1) (2) ||p|| (3) ||g|| (4) cos 6, where is the angle between p and q. (5) d(p, q) (b) Find the value of the real number t for which the polynomials p and p + tq are orthogonal.