Option 18 DHS 3.1

DHS - 3.1
№1.18. Four points A1 are given (7; 2; 2); A2 (–5; 7; -7); A3 (5; -3; 1); A4 (2; 3; 7). Create equations: a) plane A1A2A3; b) straight A1A2; c) straight A4M; perpendicular to the A1A2A3 plane; d) straight A3N; parallel straight line A1A2; e) a plane passing through point A4; perpendicular to the straight line A1A2; Calculate: e) the sine of the angle between the straight A1A4 and the plane A1A2A3; g) the cosine of the angle between the OXU coordinate plane and the A1A2A3 plane.
№ 2.18. To show that the straight line x / 6 = - (x-3) / 8 = - (z-1) / 9 is parallel to the plane x + 3y-2z + 1 = 0, and the straight line is x = 2t + 7, y = t-2, z = 2t + 1 lies in this plane.
No. 3.18. Create an equation for the plane passing through the Oz axis and the point K (-3; 1; -2) Prove the parallelism of straight lines (x -1) / 6 = (y + 2) / 2 = z / (- 1) and x – 2y + 2z – 8 = 0; x + 6z – 6 = 0.