IDZ Ryabushko 3.1 Variant 13

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IDZ Ryabushko 3.1 Variant 13

№1 Given four points A1 (4; 6; 5); A2 (6; 9; 4); A3 (2; 10; 10); A4 (7; 5; 9). Draw up the equations: a) plane A1A2A3; b) straight line A1A2; c) direct A4M; perpendicular to the plane A1A2A3; d) direct A3N; parallel line A1A2; e) the plane passing through point A4; perpendicular to the straight line A1A2; Calculate: e) the sine of the angle between the straight line A1A4 and the plane A1A2A3; g) the cosine of the angle between the Ohu coordinate plane and the A1A2A3 plane.

No. 2 Make the equation of the plane; passing through the origin perpendicular to the two planes 2x-3y + z-1 = 0 and x-y + 5z + 3 = 0.

№3 Check if A (0; 0; 2), B (4; 2; 5) lie on one straight line; and C (12; 6; 11).

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