Grade 12 solutions please

MCV 4U Name: Assignment 3: Lines & Planes Provide a full solution for each problem. 1. Determine the points of intersection of the line [x.y.z] = [0.5,3]+/[1.-3,-2]./ eR with the sphere x3 + y' + 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 + 8z + 14=0 the planes: x + 6y - 1lz -17=0 3. The origin, and the point P(10, 10, 10) are not located on the plane 3x+ 2y-z-14=0. Are they on the same side, or opposite sides of the plane? Justify your response. 4. Given a line x - 1_ e 3 = y - 2 =2-k 5 , and a plane 2x - 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