1) Suppose a, b, and c are vectors such that a x b =(2,-1,7) and a x c = (10,8,-3). Determine (3b-c) .( 2a) (dot product of this expression).

Answer: (8,22,-48).

2.)Determine the numbers a, b, and c such that the vector (a, b, c) is an unit vector with direction angles of

60.3, 34.0, and 105.

Answer: (0.50,0.83,-0.26)

3) Determine the value(s) of k such the area of the parallelogram formed by the vectors = a(1, 1, -1) and =b

(1, k, 0) is sqrt 2.

Answer: k=0 and k=1