Ryabushko A.P. IDZ 3.1 option 24

DHS - 3.1
№1.24. Given four points A1 (5; 3; 7); A2 (-2, 3, 5); A3 (4; 2; 10); A4 (1; 2; 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.
№2.24. Determine at what value B plane x - 4y + z - 1 = 0 and 2x + By + 10z - 3 = 0 are perpendicular.
№3.24. A general equation of the line formed by the intersection of the plane x + 2y - z + 5 = 0 plane passing through the axis Oy and the point M (5, 3, 2).