Ryabushko A.P. IDZ 3.1 option 22

DHS - 3.1
№1.22. Given four points A1 (4; 2; 10); A2 (1; 2; 0); A3 (3; 5; 7); A4 (2, -3 and 5). 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.
№2.22. The equation of the plane passing through the point M (2, 3, -1) and direct x = t-3; y = 2t + 5; -3t + z = 1.
№3.22. Find the point of intersection (x-7) / 5 = (y-1) / 1 = (z-5) / 4 plane and 3x-y + 2z-8 = 0.