Ryabushko A.P. IDZ 3.1 option 29

№1.29. Given four points A1 (2; 1; 7); A2 (6, 3, 1); A3 (3; 2; 8); A4 (2, -3, 7). Be the equation: a) plane A1A2A3; b) direct A1A2; c) direct A4M perpendicular to the plane A1A2A3; d) A3N straight, parallel to the line A1A2; d) a plane passing through the 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.
№2.29. Find the equation of the plane passing through the points M (2, 3, -5); N (-1; 1; -6); parallel to the vector a = (4; 4; 3).
№3.29. Be the canonical equation of the line passing through the point M (1, -5, 3) perpendicular to the line ... and x = 3t + 1; -t-y = 5; z = 2t + 3.