Option 7 DHS 3.1

Option 7 DHS 3.1

№1.7. There are four points A1 (5; 5; 4); A2 (1; –1; 4); A3 (3; 5; 1); A4 (5; 8; –1). Create equations: a) plane A1A2A3; b) straight A1A2; c) direct A4M; perpendicular to the A1A2A3 plane; d) straight A3N; parallel straight line A1 A2; e) a plane passing through point A4; perpendicular to the straight A1A2. Calculate: e) the sine of the angle between the straight line A1A4 and the plane A1A2A3; g) the cosine of the angle between the OXU coordinate plane and the A1A2A3 plane.
№2.7. Make an equation for a plane passing through point A (3; 4; 0) and a straight line .....
No. 3.7. Find the point of intersection of the line .... and the plane 2x + 3y + z - 1 = 0.