# IDZ 3.1 - Option 10. Decisions Ryabushko AP

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# Description

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;
1.10 A1 (6, 8, 2), A2 (5, 4, 7), A3 (2, 4, 7), A4 (7, 3, 7)

2. Solve the following tasks
2.10 in the equation of the plane "segments", if it passes through the point M (6, -10, 1) and intercepts the axis Ox segment a = -3, and on the axis Oz - segment c = 2

3. Solve the following tasks
3.10 At what value of A plane Ax + 3y - 5z + 1 = 0 is parallel to the line (x-1) / 4 = (y + 2) / 3 = z / 1?