Option 20 DHS 3.1

Option 20 DHS 3.1

№1.20. There are four points A1 (1; –1; 3); A2 (6; 5; 8); A3 (3; 5; 8); A4 (8; 4; 1). 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;
№2.20. Make a plane equation; passing through the axis Oy and point M (3; –5; 2).
№3.20. At what value of D is the line .... intersects the axis Oz?