Option 16 DHS 3.1

Option 16 DHS 3.1

№1.16. There are four points A1 (1; 8; 2); A2 (5; 2; 6); A3 (5; 7; 4); A4 (4; 10; 9). 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.
No. 2.16. Find the values ​​of the segments cut off on the coordinate axes by the plane passing through the point M (2; –3; 3) parallel to the plane 3x + y – 3z = 0.
No. 3.16. For what values ​​of A and B is the plane Ax + By + 6z - 7 = 0 perpendicular to the straight line ...?