Option 6 DHS 3.1

№1.6. Given the four points A1 (0; 7; 1); A2 (2; –1; 5); A3 (1; 6; 3); A4 (3; –9; 8). Create equations: a) plane A1A2A3; b) straight A1A2; c) direct A4M; perpendicular to the A1A2A3 plane; d) straight A3N; parallel 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 line A1A4 and the plane A1A2A3; g) cosine of the angle between the coordinate plane Oxu and the plane A1A2A3;
№2.6. Create an equation for the plane; passing through points A (2; 5; –1) and B (–3; 1; 3) parallel to the axis Oy.
№3.6. At what value is the line ....; parallel to the line .....