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IDZ Ryabushko 3.1 Variant 2

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IDZ Ryabushko 3.1 Variant 2

№1 Given four points A1 (3; –1; 2); A2 (–1; 0; 1); A3 (1; 7; 3); A4 (8; 5; 8). 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) a 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 A1 plane A2A3;

№2 Make an equation for the plane passing through the middle of the segment M1M2 perpendicular to this segment, if M1 (1; 5; 6); M2 (–1; 7; 10).

№3 Prove that the line ...... is parallel to the plane 2x + y - z = 0; and the line ..... lies in this plane.

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