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IDZ Ryabushko 3.1 Variant 5

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IDZ Ryabushko 3.1 Variant 5

№1 Given four points A1 (9; 5; 5); A2 (–3; 7; 1); A3 (5; 7; 8); A4 (6; 9; 2). 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
plane A1A2A3.

№2 Make an equation for the plane passing through the axis Ox and point A (2; 5; –1).

№3 Draw up the parametric equations of the median of the triangle with the vertices A (3; 6; –7); B (–5; 1; –4); C (0; 2; 3); drawn from vertex C.

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