# Version 3.1 Collection of 23 DHS DHS Ryabushko

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# Description

№1.23. Given four points A1 (2; 3; 5); A2 (5; 3, -7); A3 (1; 2; 7); A4 (4, 2, 0). Be the equation: a) plane A1A2A3; b) direct A1A2; c) direct A4M; perpendicular to the plane of A1A2A3; d) A3N straight, parallel to the line A1A2; d) a plane passing through A4; perpendicular to the line A1A2. Calculate: e) The sine of the angle between the line and the plane A1A4 A1A2A3; g) the cosine of the angle between the coordinate plane and the plane Oxy A1A2A3.
№2.23. Find the projection of M (4; -3; 1) on the plane x - 2y - z - 15 = 0.
№3.23 the equation of the plane passing through the point K (2 - 5 3) parallel to the plane Oxz.