Option 13 DHS 3.1

DHS - 3.1
№1.13. Given the four points A1 (4; 6; 5); A2 (6; 9; 4); A3 (2; 10; 10); A4 (7; 5; 9). 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 line A1A4 and the plane A1A2A3; g) the cosine of the angle between the OXU coordinate plane and the A1A2A3 plane.
№2.13. Create an equation for the plane; passing through the origin perpendicular to the two planes 2x-3y + z-1 = 0 and x-y + 5z + 3 = 0.
№3.13. Check whether A (0; 0; 2), B (4; 2; 5) lie on one straight line; and C (12; 6; 11).