Option 29 DHS 3.1

Option 29 DHS 3.1

№1.29. Four points are given A1 (2; –1; 7); A2 (6; 3; 1); A3 (3; 2; 8); A4 (2; –3; 7). Create equations: a) plane A1A2A3; b) straight A1A2; c) straight A4M, perpendicular to the A1A2A3 plane; d) straight A3N parallel to straight line A1A2; e) a plane passing through the 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 coordinate plane Oxu and the plane A1A2A3.
№2.29. Create an equation for the plane passing through the points M (2; 3; –5); N (–1; 1; –6); parallel to the vector a = (4; 4; 3).
№3.29. Create a canonical equation of a straight line passing through the point M (1; –5; 3) perpendicular to the straight lines ... and x = 3t + 1; y = –t – 5; z = 2t + 3.