Option 24 DHS 3.1

DHS - 3.1
№1.24. Four points A1 are given (5; 3; 7); A2 (–2; 3; 5); A3 (4; 2; 10); A4 (1; 2; 7). 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 A1A4 and the plane A1A2A3; g) the cosine of the angle between the coordinate plane Oxu and the plane A1A2A3.
№2.24. Determine for what value of B the planes x - 4y + z - 1 = 0 and 2x + By + 10z - 3 = 0 will be perpendicular.
No. 3.24. Create a general equation of a line formed by the intersection of the plane x + 2y - z + 5 = 0 with the plane passing through the axis Oy and the point M (5; 3; 2).