IDZ Ryabushko 3.1 Variant 12

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IDZ Ryabushko 3.1 Variant 12

№1 Given four points A1 (4; 4; 10); A2 (7; 10; 2); A3 (2; 8; 4); A4 (9; 6; 9). Draw up the equations: a) plane A1 A2 A3; b) straight line A1A2; c) a straight line A4M perpendicular to the plane A1A2A3; d) line A3N parallel to line A1A2; e) a plane passing through point A4, perpendicular to the 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 Make an equation for the plane passing through points A (1; 1; 0) and B (2; –1; –1) perpendicular to the plane 5x + 2y + 3z - 7 = 0.

№3 Make an equation of a line passing through the origin parallel to the line x = 2t + 5; y = - 3t + 1; z = - 7t - 4.

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