Version 19 DHS 3.1

№1.19. Four points are given A1 (8; –6; 4); A2 (10; 5; –5); A3 (5; 6; –8); A4 (8; 10; 7). 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 the 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 coordinate plane Oxu and the plane A1A2A3;
№2.19. Make a general equation of a plane passing through point A (3; –4; 1) parallel to the coordinate plane Oxz.
№3.19. Show that straight .... and ....; perpendicular.