Option 12 DHS 3.1

Option 12 DHS 3.1

№1.12. Given the four points A1 (4; 4; 10); A2 (7; 10; 2); A3 (2; 8; 4); A4 (9; 6; 9). Create equations: a) the plane A1 A2 A3; b) straight A1A2; c) straight A4M, perpendicular to the A1A2A3 plane; d) straight A3N parallel to straight line A1A2; e) a plane passing through point A4, perpendicular to the 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.
№2.12. Compose the equation of the plane passing through the points A (1; 1; 0) and B (2; –1; –1) perpendicular to the 5x + 2y + 3z plane - 7 = 0.
№ 3.12. Create an equation of a straight line passing through the origin parallel to the straight line x = 2t + 5; y = - 3t + 1; z = - 7t - 4.