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;
 1.23 A1 (2, 3, 5), A2 (5, 3, -7), A3 (1, 2, 7), A4 (4, 2, 0)

2. Solve the following tasks
 Find the projection of 2.23 M (4, 3, 1) in the plane x - 2y - z-15 = 0

3. Solve the following tasks
 3.23 Write the equation of the plane passing through the point K (2, -5, 3) parallel to the plane Oxz.

Detailed solution. Designed in PDF format for easy viewing of IDZ solutions on smartphones and PCs. In MS Word (doc format) sent additionally.