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IDZ Ryabushko 3.1 Variant 9

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IDZ Ryabushko 3.1 Variant 9

№1 Given four points A1 (7; 5; 3); A2 (9; 4; 4); A3 (4; 5; 7); A4 (7; 9; 6). 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.

№2 Draw up the general equations of the line formed by the intersection of the plane 3x - y - 7z + 9 = 0; with a plane passing through the axis Ox and point A (3; 2; –5).

No. 3 At what value of the C plane 3x - 5y + Cz - 3 = 0; and x + 3y + 2z + 5 = 0 are perpendicular.

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