1. Consider the three vectors 5: (2,3,1), b= (3, -2, 1) and E = (1,8,3) a) Compute the angle between a and b (5 points) b) Prove that vectors ii, 3 and 5 lie in the same plane. (5 points) 2. Calculate the area of the parallelogram with 2 adjacent sides formed by the vectors 51' = (1,2,0) and 5; = (1,0,2). (5 points) b) d) A curve is given by t) = (126050), 125in(t), 5t). Compute the unit tangent vector, 't) (3 points) the principal unit normal vector, 1'70). (4 points) the binormal vector, I? (t) = t) x IV (t). (4 points) the curvature of the curve. Give a reason for your answer. (4 points) 12. Find the equation of the tangent plane to the surface x- + y - z = 49 at (5, 5, 1). (5 points) 13. Determine the relative maxima/minima/saddle points of the function given by f(x,y) = 2x4 - xy + 2y. (10 points)6 of 6 14. Using Lagrange multipliers, find the extrema of f(x, y) = x + 2y subject to the constraint x + y =5. (6 points)