IDZ 3.1 - Option 2. 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;
 1.2 A1 (3, -1, 2), A2 (-1, 0, 1), A3 (1, 7, 3), A4 (8, 5, 8)

2. Solve the following tasks
 2.2 Create equation of the plane passing through the midpoint of the segment M1M2 perpendicular to this segment, if M1 (1, 5, 6), M2 (-1, 7, 10).

3. Solve the following tasks
 3.2 Prove that the line (x + 1) / 2 = (y + 1) / - 1 = (z-3) / 3 is parallel to the plane of 2x + y - z = 0, and (x-2) / 2 = y / -1 = (z-4) / 3 line lies in the plane