Option 25 DHS 3.1

Option 25 DHS 3.1

DHS - 3.1
No. 1.25. There are four points A1 (4; 3; 5); A2 (1; 9; 7); A3 (0; 2; 0); A4 (5; 3; 10). Create equations: a) plane A1A2A3; b) straight A1A2; c) straight A4M; perpendicular to the A1A2A3 plane; d) straight A3N; parallel straight line A1A2; e) a plane passing through point A4; perpendicular to the straight line A1A2; Calculate: e) the sine of the angle between the straight A1A4 and the plane A1A2A3; g) the cosine of the angle between the OXU coordinate plane and the A1A2A3 plane.
№2.25. Create an equation for the plane that passes the point M (2; –3; –4) and cuts off non-zero segments of the same length on the coordinate axes.
№3.25. For what values ​​of B and D is the straight line x – 2y + z – 9 = 0; 3x + By + z + D = 0; lies in the Oxy plane.