IDZ 3.1 - Option 30. 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;
 1.30 A1 (0, 4, 5), A2 (3, 2, 1), A3 (4, 5, 6), A4 (3, 3, 2)

2. Solve the following tasks
 2.30 To determine at what value C plane 3x-5y + Cz-3 = 0 and x-3y + 2z + 5 = 0 are perpendicular?

3. Solve the following tasks
 3.30 Find point symmetric M (4, 3, 10) relative to the line (x-1) / 2 = (y-2) / 4 = (z-3) / 5