Option 8 DHS 3.1

№1.8. Four points A1 are given (6; 1; 1); A2 (4; 6; 6); A3 (4; 2; 0); A4 (1; 2; 6). Create equations: a) plane A1A2A3; b) straight A1A2; c) direct A4M; perpendicular to the A1A2A3 plane; d) straight A3N; parallel straight line A1A2; 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.
№2.8. Create an equation for a plane passing through two parallel lines: .... and ....
# 3.8. Find the projection of the point P (3; 1; –1) on the plane .....