IDZ 3.1 - Option 21. 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;

1.21 A1 (1, 2, 7), A2 (4, 2, 10), A3 (2, 3, 5), A4 (5, 3, 7)


2. Solve the following tasks

2.21 Write the equation of the plane passing through the points M (1; 2; 3) and N (-3; 4, -5) parallel to the axis Oz


3. Solve the following tasks

3.21 At what value of p lines x = 2t + 5, y = -t + 2, z = pt-7 x + 3y + z + 2 = 0 xy-3z-2 = 0 parallel?