IDZ 3.1 - Option 19. 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;
 1.19 A1 (8, -6, 4), A2 (10, 5, -5), A3 (5, 6, -8), A4 (8, 10, 7)

2. Solve the following tasks
 2.19 a general equation of the plane passing through the point A (3, -4, 1) parallel to the plane Oxz.

3. Solve the following tasks
 3.19 Show that the lines x / 1 = (y-1) / - 2 = z / 3 and 3x + y-5z + 1 = 0, 2x + 3y-8z + 3 = 0 perpendicular