Option 23 DHS 3.1

№1.23. There are four points A1 (2; 3; 5); A2 (5; 3; –7); A3 (1; 2; 7); A4 (4; 2; 0). 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 A1A2. Calculate: e) the sine of the angle between the straight A1A4 and the plane A1A2A3; g) the cosine of the angle between the coordinate plane Oxu and the plane A1A2A3.
№2.23. Find the projection of the point M (4; –3; 1) on the plane x - 2y - z - 15 = 0.
№3.23. Compose the equation of the plane passing through the point K (2; - 5; 3) parallel to the plane Oxz.