IDZ 3.1 - Option 22. 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;
 1.22 A1 (4, 2, 10), A2 (1, 2, 0), A3 (3, 5, 7), A4 (2, 3, 5)

2. Solve the following tasks
 2.22 Create equation of the plane passing through the point M (2, 3, -1) and direct x = t-3, y = 2t + 5, z = -3t + 1.

3. Solve the following tasks
 3.22 Find the point of intersection (x-7) / 5 = (y-1) / 1 = (z-5) / 4 and the plane 3x - y + 2z-8 = 0