IDZ 3.1 - Option 29. 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;
 1.29 A1 (2, 1, 7), A2 (6, 3, 1), A3 (3, 2, 8), A4 (2, 3, 7)

2. Solve the following tasks
 2.29 Write the equation of the plane passing through the points M (2, 3, -5), N (-1, 1, -6) parallel to the vector a = (4, 4, 3)

3. Solve the following tasks
 3.29 Be the canonical equation of the line passing through M (1, -5, 3) perpendicular to the line x / 2 = (y-2) / 3 = (z + 1) / - 1 and x = 3t + 1, y = -t-5, z = 2t + 3