Option 22 DHS 3.1

Option 22 DHS 3.1

DHS - 3.1
№1.22. There are four points A1 (4; 2; 10); A2 (1; 2; 0); A3 (3; 5; 7); A4 (2; –3; 5). Create equations: a) plane A1A2A3; b) straight A1A2; c) straight A4M; perpendicular to the A1A2A3 surface; 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 A1A4 and the plane A1A2A3; g) the cosine of the angle between the OXU coordinate plane and the A1A2A3 plane.
№2.22. Create an equation for the plane passing through the point M (2; 3; –1) and the line x = t – 3; y = 2t + 5; z = –3t + 1.
№3.22. Find the intersection point of the line (x-7) / 5 = (y-1) / 1 = (z-5) / 4 and the 3x – y + 2z – 8 = 0 plane.