Option 10 DHS 3.1

DHS - 3.1
№1.10. There are four points A1 (6; 8; 2); A2 (5; 4; 7); A3 (2; 4; 7); A4 (7; 3; 7). 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 coordinate plane Oxu and the plane A1A2A3.
No. 2.10. Make a plane equation in “segments” if it passes through the point M (6; –10; 1) and cuts the segment a = –3 on the Ox axis; and on the axis Oz - segment c = 2.
№ 3.10. At what value A, the plane Ax + 3y– 5z + 1 = 0 is parallel to a straight line .....