IDZ 3.1 - Option 12. 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;
 1.12 A1 (4, 4, 10), A2 (7, 10, 2), A3 (2, 8, 4), A4 (9, 6, 9)

2. Solve the following tasks
 2.12 Write the equation of the plane passing through the points A (1, 1, 0), B (2, -1, -1) is perpendicular to the plane 5x + 2y + 3z - 7 = 0

3. Solve the following tasks
 3.12 Write the equation of the line passing through the origin parallel to the line x = 2t + 5, y = -3t + 1, z = -7t - 4