1) (10 points) Let a = -1i + 2 + 2k and b = 2i - j + k. a) (3 points) Find a . b b) (3 points) Find the angle between vectors a and b c) (4 points) Find a vector perpendicular to vectors a and b\f2) (10 points) Let z = 4x*+y? be a quadric surface. a) (2 points) Sketch the surface. What type of quadric surface does this equation represent? b) (4 points) Find the equation of the tangent plane to the surface at (1, 1, 5). c) (4 points) Find the equation of the line that is perpendicular to the surface at (1,1,5). \f4) (10 points) A projectile is fired with an initial speed (vo) of 175 m/s, at an angle a of 30 degrees, and at a position 600 m above ground level. Based on Newton's 2" Law and assuming no air resistance, the position vector of the projectile is: r(t) = (vocosa)ti + [ro+(vesina)t - 1/2gt?)]j where time t = 0, ry is the initial height above ground surface, and the acceleration of gravity g = 9.81 m/s?. Where does the projectile hit the ground and with what speed? 5) (10 points) Find the work done by the force field F =-yz i + xz j +xy k as the point of application moves from point A (1,0,0) to the point B (1,0,2It) a) (4 points) along the circular helix C1 parameterized by: r(t) = cos(t) i+ sin(t) j + t k for 0 S t = 2n b) (4 points) along the line segment AB parameterized by: r(t) = i+ tk for 0