IDZ 3.1 - Option 3. 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;
 1.3 A1 (3, 5, 4), A2 (5, 8, 3), A3 (1, 2, -2), A4 (-1, 0, 2)

2. Solve the following tasks
 2.3 Find the distance from point M (2, 0, -0.5) to the plane 4x - 4y + 2z + 17 = 0

3. Solve the following tasks
 3.3 Write the equation of the line passing through the point M (1, -3, 3) and forming an angle with the coordinate axes, respectively equal to 60◦, 45◦, 120◦.