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IDZ Ryabushko 3.1 Variant 18

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IDZ Ryabushko 3.1 Variant 18

№1 Given four points A1 (7; 2; 2); A2 (–5; 7; -7); A3 (5; -3; 1); A4 (2; 3; 7). 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 Show that line x / 6 = - (x-3) / 8 = - (z-1) / 9 parallel to the plane x + 3y-2z + 1 = 0, and line x = 2t + 7, y = t- 2, z = 2t + 1 lies in this plane.

№3 Make an equation for the plane passing through the Oz axis and the point K (-3; 1; -2) Prove the parallelism of the lines (x -1) / 6 = (y + 2) / 2 = z / (- 1) and x– 2y + 2z – 8 = 0; x + 6z – 6 = 0.

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