Option 15 DHS 3.1

№1.15. There are four points A1 (10; 9; 6); A2 (2; 8; 2); A3 (9; 8; 9); A4 (7; 10; 3). Create equations: a) plane A1A2A3; b) straight A1A2; c) straight A4M, perpendicular to the A1A2A3 plane; d) straight A3N parallel to straight line A1A2; e) a plane passing through point A4, perpendicular to the 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.
No. 2.15. Create an equation for a plane passing through the origin perpendicular to the vector AB, if A (5; –2; 3); B (1; –3; 5).
№3.15. Create an equation of a straight line passing through the point M (2; –3; 4-) perpendicular to the straight lines ..... and .....