IDZ 3.1 - Option 8. 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;

1.8 A1 (6, 1, 1), A2 (4, 6, 6), A3 (4, 2, 0), A4 (1, 2, 6)


2. Solve the following tasks

2.8 Create equation of the plane passing through the two parallel straight lines (x-3) / 2 = y / 1 = (z-1) / 2 and (x + 1) / 2 = (y-1) / 1 = z / 2.


3. Solve the following tasks

3.8 Find the projection of point P (3, 1, -1) on a plane x + 2y + 3z-30 = 0