HELP I REALLY NEED CALCULUS VECTORS HELP!!! FULL ANSWERS PLEASE

Provide a full solution for each problem. 1. Determine the points of intersection of the line [x,y,z] = [0,5,3]+t[1,3,2],t r-_' R with the sphere .r2 + y2 + :2 = 6 . Is the segment of the line between the intersection points a diameter of the sphere? 2. Determine the components of a vector of length 12 that lines on the line of intersection of 2x y + 8g +14=0 the Planes; x + 6y llz 17=0 3. The origin, and the point PUD, 10, 10) are not located on the plane 31: + Zy z 14 = 0. Are they on the same side, or opposite sides of the plane? Justify your response. 4. Given a line 21 = y - 2 = 2%k , and a plane 2;; y z +10 = 0,determine values of k, if possible, such that the line and the plane intersect: a) never b) at an infinite number of points c) at one point