IDZ 3.1 - Option 11. 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;
 1.11 A1 (4, 2, 5), A2 (0, 7, 1), A3 (0, 2, 7), A4 (1, 5, 0)

2. Solve the following tasks
 2.11 Create equation of the plane passing through A (2, 3, 4) parallel to the two vectors a = (4, 1, -1) and b = (2, -1, 2)

3. Solve the following tasks
 At what value of 3.11 m and with direct (x-2) / m = (y + 1) / 4 = (z-5) / - 3 perpendicular to the plane 3x-2y + Cz + 1 = 0?