 # Version 3.1 Collection of 12 DHS DHS Ryabushko

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