Ryabushko A.P. IDZ 3.1 option 1

DHS - 3.1
№1.1. Given four points A1 (3; 1; 4); A2 (1; 6; 1); A3 (-1, 1, 6); A4 (0, 4, 1). Be the equation: a) plane A1A2A3; b) direct A1A2; c) direct A4M; perpendicular to the plane of A1A2A3; g) direct A3N; parallel line A1A2; d) a plane passing through A4; perpendicular to the line A1A2; Calculate: e) The sine of the angle between the line and the plane A1A4 A1A2A3; g) the cosine of the angle between the coordinate plane and the plane Oxy A1A2A3.
№2.1. Find the intercept on the coordinate axes plane passing through the point M (-2; 7, 3) parallel to the x -4y + 5z - 1 = 0.
№3.1. Prove parallel lines (x -1) / 6 = (y + 2) / 2 = z / (- 1) and x-2y + 2z-8 = 0; x + 6z-6 = 0.