Option 17 DHS 3.1

Option 17 DHS 3.1

№1.17. Four points A1 are given (6; 6; 5); A2 (4; 9; 5); A3 (4; 6; 11); A4 (6; 9; 3). 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;
№2.17. Create an equation for the plane passing through the point M (1; –1; 2) perpendicular to the segment M1M2; if M1 (2; 3; –4); M2 (–1; 2; –3).
№3.17. Show that the straight line is parallel to the plane x + 3y - 2z + 1 = 0; and the straight line is x = t + 7; y = t - 2; z = 2t + 1 lies in this plane.