Option 9 DHS 3.1

Option 9 DHS 3.1

№1.9. There are four points A1 (7; 5; 3); A2 (9; 4; 4); A3 (4; 5; 7); A4 (7; 9; 6). 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 line A1A4 and the plane A1A2A3; g) the cosine of the angle between the OXU coordinate plane and the A1A2A3 plane.
№2.9. Create general equations of the line formed by the intersection of the plane 3x - y - 7z + 9 = 0; with the plane passing through the axis Ox and point A (3; 2; –5).
No. 3.9. At what value C of the plane 3x - 5y + Cz - 3 = 0; and x + 3y + 2z + 5 = 0 are perpendicular.