1 Find the angle between the vectors < 2, 1, 1 > and < 1, 2, 1 >.

 2 Find the angles of the triangle whose vertices are P = (2, 3, 0), Q = (5, 3, 1), and R = (4, 3, 4).

 3 For which values of t, if any, will the vectors < t, 3, 1 > and < 1, 1, 3 >: (a). be orthogonal? (b). form an acute angle? (i.e. the angle between them is less than 90 degrees.)

  4 Let P = (1, 1, 4), Q = (1, t 1, 0), and R = (9, t 1, 2). For which values of t, if any, will the angle between the vectors PQ and PR (a). be an acute angle? (b). be a right angle?

  5 Find the scalar projection and vector projection of b =< 2, 7, 4 > onto a =< 3, 0, 4 >.