Ryabushko A.P. IDZ 3.1 option 21

DHS - 3.1
№1.21. Given four points A1 (1, -2, 7); A2 (4; 2; 10); A3 (2; 3; 5); A4 (5; 3; 7). 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.
№2.21. Find the equation of the plane; which passes through the point M (1; 2; 3) and N (-3, 4, -5) parallel to the axis z.
№3.21. At what value of direct p; the lines are parallel.