IDZ 3.1 - Option 14. 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;
 1.14 A1 (3, 5, 4), A2 (8, 7, 4), A3 (5, 10, 4), A4 (4, 7, 8)

2. Solve the following tasks
 2.14 Write the equation of the plane passing through the points A (3, -1, 2), B (2, 1, 4) parallel to the vector a = (5, -2, -1)

3. Solve the following tasks
 3.14 Write the equation of the line passing through the point M (2, -5, 3) parallel to the line 2x - y + 3z - 1 = 0, 5x + 4y - z - 7 = 0