Option 27 DHS 3.1

No. 1.27. There are four points A1 (2; 1; 6); A2 (1; 4; 9); A3 (2; –5; 8); A4 (5; 4; 2). 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 A1A2. Calculate: e) the sine of the angle between the straight A1A4 and the plane A1A2A3; g) the cosine of the angle between the coordinate plane Oxu and the plane A1A2A3.
No. 2.27. Create an equation for the plane passing through the points A (2; 3; –1); B (1; 1; 4); perpendicular to the plane x - 4y + 3z + 2 = 0.
№ 3.27. Make an equation of a straight line passing through the point E (3; 4; 5) parallel to the axis Ox.