Option 11 DHS 3.1

Option 11 DHS 3.1

№1.11. Given the four points A1 (4; 2; 5); A2 (0; 7; 1); A3 (0; 2; 7); A4 (1; 5; 0). 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) the cosine of the angle between the OXU coordinate plane and the A1A2A3 plane.
№ 2.11. Make an equation for a plane passing through point A (2; 3; –4) parallel to two vectors a = {4; one; -one }; c = {2; -one; 2}.
№ 3.11. Under what conditions m and C is the line perpendicular to the 3x - 2 y + Cz + 1 = 0 plane?