I. Let .51.: {1], 2. 1} and E = {1,1,1}_ Find the following: -I |. 1. A unit vector parallel to EA H. 2. The scalar fl:- 3 x E. 1 . - .. 3. The component of EA in the direction of i x j. 4. A unit vector orthogonal to fl. and whose representations are parallel to the yzpiane. II. Find an equation of the plane containing the points [11.2. 1] and (l. 1. 1] and perpendicular to the plane 2:: z = ll. III. Find a set of equations of the line passing through (21, 2. 1] and parallel to the line of intersection of the planesr gr+22+d=and 23+3y+z12={l. IV. 1. Sketch the cylinder described by the equation 23:3; y 1 = . 2. Sketch and identify the graph of the surface of revolution generated by revolving 31:: + dz 12 = [1 about the uraxis and nd the equation of this surface of revolution. 3. In each of the following, identify the quadric surface and draw a sketch of the graph as indicated. {a} 3.522 92:2 + fly\" 35 = fl {identityt and sketch) [b] 32::2 z\" + 53: + 12y + dz 1 = [l {identify only)