IDZ 3.1 - Option 15. 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;
 1.15 A1 (10, 9, 6), A2 (2, 8, 2), A3 (9, 8, 9), A4 (7, 10, 3)

2. Solve the following tasks
 2.15 Create equation of the plane through the origin perpendicular to the vector AB, if A (5, 2, 3), B (1, 3, 5).

3. Solve the following tasks
 3.15 Write the equation of the line passing through the point M (2, 3, 4) perpendicular to the right (x + 2) / 1 = (y-3) / - 1 = (z + 1) / 1 (x + 4) / 2 = y / 1 = (z-4) / - 3