IDZ 3.1 - Option 17. 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;

1.17 A1 (6, 6, 5), A2 (4, 9, 5), A3 (4, 6, 11), A4 (6, 9, 3)


2. Solve the following tasks

2.17 Create equation of the plane passing through the point M (1, -1, 2) perpendicular to the line segment M1M2, if M1 (2, 3, -4), M2 (-1, 2, -3).


3. Solve the following tasks

3.17 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.