Ryabushko A.P. IDZ 3.1 option 14

№1.14. Given four points A1 (3; 5; 4); A2 (8, 7, 4); A3 (5; 10; 4); A4 (4; 7; 8). Be the equation: a) plane A1A2A3; b) direct A1A2; c) direct A4M; perpendicular to the plane of A1A2A3; d) A3N straight, parallel to the line A1A2; d) a plane passing through the point A4; perpendicular to the line A1 A2. 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.
№2.14. Find the equation of the plane passing through point A (3; 1; 2); B (2, 1, 4) parallel to the vector a = (5, -2, -1).
№3.14 the equation of the line passing through the point M (2, -5, 3); parallel to the line 2x - y + 3z - 1 = 0; 5x + 4y - z - 7 = 0.