Option 1 DHS 3.1

Option 1 DHS 3.1

DHS - 3.1
№1.1. Given the four points A1 (3; 1; 4); A2 (–1; 6; 1); A3 (–1; 1; 6); A4 (0; 4; –1). Create equations: a) plane A1A2A3; b) straight A1A2; c) straight A4M; perpendicular to the A1A2A3 plane; d) straight A3N; parallel straight line A1A2; e) a plane passing through point A4; perpendicular to the straight 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.
№ 2.1. Find the values ​​of the segments cut off on the coordinate axes by the plane passing through the point M (–2; 7; 3) parallel to the plane x –4y + 5z - 1 = 0.
No.3.1. Prove parallelism of straight lines (x -1) / 6 = (y + 2) / 2 = z / (- 1) and x – 2y + 2z – 8 = 0; x + 6z – 6 = 0.