IDZ 3.1 - Option 24. Decisions Ryabushko AP

1. Given four points A1 (x1, y1, z1), A2 (x2, y2, z2), A3 (x3, y3, z3), A4 (x4, y4, z4)
 Be the equation:
 a) a plane A1A2A3; b) direct A1A2;
 c) direct A4M perpendicular to the plane A1A2A3;
 g) direct A3N, parallel line A1A2;
 d) a plane passing through the point perpendicular to the line A4 A1A2.
 Calculated:
 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;
 1.24 A1 (5, 3, 7), A2 (-2, 3, 5), A3 (4, 2, 10), A4 (1, 2, 7)

2. Solve the following tasks
 2.24 To determine at what value B plane x-4y + z-1 = 0 and 2x + By + 10z-3 = 0 are perpendicular?

3. Solve the following tasks
 3.24 Create the 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)