IDZ 3.1 - Option 7. 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;
 1.7 A1 (5, 5, 4), A2 (1, 1, 4), A3 (3, 5, 1), A4 (5, 8, -1)

2. Solve the following tasks
 2.7 Create equation of the plane passing through point A (3; 4; 0) and a line (x-2) / 1 = (y-3) / 2 = (z + 1) / 2.

3. Solve the following tasks
 3.7 Find the point of intersection (x-1) / 1 = (y + 1) / - 2 = z / 6 and the plane 2x + 3y + z-1 = 0