1. Given a = [2,5, -7] and b = [3, -6, -2], find (4 marks) a. a . b b. A unit vector in the direction of 7. c. The angle between a and b. d. A vector perpendicular to a 2. A force F = [-2,1,5] in Newtons, pulls a sled through a displacement s = [-3, 5, 4] in metres. The link between the dot product and geometric vectors and the calculation of work is (2 marks) Work = F 8 cos ( 0 ) . a. How much work is done on the sled by the force? b. What is the minimum magnitude of force that could have been applied to the sled to obtain the same work? Explain your answer. 3. Given a = [1, -3,6] and b = [4, -5, -2], find (4 marks) a. a x b and verify that it is perpendicular to both a and b. b. A vector c such that a . (b x c ) = 0. What is the relationship between the vectors a, b, and c in this case, and why? Verify this