IDZ 3.1 - Option 1. 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;
 1.1 A1 (3, 1, 4), A2 (-1, 6, 1), A3 (-1, 1, 6), A4 (0, 4, 1)

2. Solve the following tasks
 2.1 Find the intercept on the coordinate axes plane passing through the point M (-2, 7, 3) parallel to the plane x - 4y + 5z - 1 = 0

3. Solve the following tasks
 3.1 Prove parallel lines (x-1) / 6 = (y + 2) / 2 = z / -1 and x - 2y + 2z - 8 = 0, x + 6z - 6 = 0