IDZ 3.1 - Option 18. 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;
 1.18 A1 (7, 2, 2), A2 (-5, 7, -7), A3 (5, 3, 1), A4 (2, 3, 7)

2. Solve the following tasks
 2.18 Show that the line x / 6 = (y-3) / 8 = (z-1) / 9 parallel to the plane x + 3y - 2z - 1 = 0, and the line x = t + 7, y = t-2, z = 2t + 1 lies in that plane.

3. Solve the following tasks
 3.18 Write the equation of the plane passing through the axis Oz and point K (-3, 1, -2)