Option 14 DHS 3.1 Collection of DHS Ryabushko

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Option 14 DHS 3.1 Collection of DHS Ryabushko

№1.14. There are four points A1 (3; 5; 4); A2 (8; 7; 4); A3 (5; 10; 4); A4 (4; 7; 8). Create equations: a) plane A1A2A3; b) straight A1A2; c) direct A4M; perpendicular to the A1A2A3 plane; d) straight A3N parallel to straight line A1A2; e) a plane passing through point A4; perpendicular to the straight line A1 A2. Calculate: e) the sine of the angle between the straight line A1A4 and the plane A1A2A3; g) the cosine of the angle between the OXU coordinate plane and the A1A2A3 plane.
No. 2.14. Create an equation for the plane passing through the points A (3; –1; 2); B (2; 1; 4) parallel to the vector a = (5; –2; –1).
№3.14. Compose the equation of a straight line passing through the point M (2; –5; 3); parallel to the straight line 2x - y + 3z - 1 = 0; 5x + 4y - z - 7 = 0.

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