Ryabushko A.P. IDZ 3.1 option 11

№1.11. Given four points A1 (4; 2; 5); A2 (0, 7, 1); A3 (0, 2, 7); A4 (1, 5, 0). Be the equation: a) plane A1A2A3; b) direct A1A2; c) direct A4M; perpendicular to the plane of A1A2A3; g) direct A3N; parallel line A1A2; d) a plane passing through 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.
№2.11. The equation of the plane passing through point A (2; 3; 4) in parallel with two vectors a = {4; 1; -1 }; B = {2; -1; 2}.
№3.11. Under what conditions m and C line perpendicular to the plane 3x - 2 y + Cz + 1 = 0.