Ryabushko A.P. IDZ 3.1 option 18

DHS - 3.1
№1.18. Given four points A1 (7, 2, 2); A2 (-5, 7, -7); A3 (5, -3, 1); A4 (2; 3; 7). Be the equation: a) plane A1A2A3; b) direct A1A2; c) direct A4M; perpendicular to the plane of A1A2A3; g) direct A3N; parallel line A1A2; d) a plane passing through A4; perpendicular to the line A1A2; Calculate: e) The sine of the angle between the line and the plane A1A4 A1A2A3; g) the cosine of the angle between the coordinate plane and the plane Oxy A1A2A3.
№2.18. Show that the line x / 6 = - (x-3) / 8 = - (z-1) / 9 parallel to the plane x + 3y-2z + 1 = 0, and the line x = 2t + 7, y = t-2, z = 2t + 1 lies in that plane.
№3.18. Find the equation of the plane through the Oz axis and the point K (-3; 1; -2) Prove parallel lines (x -1) / 6 = (y + 2) / 2 = z / (- 1) and x-2y + 8-2z = 0; x + 6z-6 = 0.