Option 2 DHS 3.1

№1.2. There are four points A1 (3; –1; 2); A2 (–1; 0; 1); A3 (1; 7; 3); A4 (8; 5; 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 A1 A2A3;
№2.2. Create an equation for the plane passing through the middle of the segment M1M2 perpendicular to this segment, if M1 (1; 5; 6); M2 (–1; 7; 10).
№ 3.2. Prove that the straight line ...... is parallel to the plane 2x + y - z = 0; and the straight line ..... lies in this plane.