[1) (5 points) Find an equation of the sphere with center (1,3,4) that is tangent to the sagplane. [2) Given the vectors u = (4, 2, 2), v = {1, 1, 3) and W = (1, 1,1). (a) (5 points) Find the unit vector in the direction of the vector 311 + 2w. (b) (5 points) Find the cosine of the angle between the vectors v and k. (c) (5 points) Find the projection of v onto w. (d) (5 points) Find the vector component of v which is orthogonal to w