Ryabushko A.P. IDZ 3.1 option 15

№1.15. Given four points A1 (10, 9, 6); A2 (2; 8; 2); A3 (9; 8; 9); A4 (7; 10; 3). 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 point 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.
№2.15. Find the equation of the plane through the origin perpendicular to the vector AB if A (5, -2, 3); B (1, -3; 5).
№3.15. Find the equation of the line passing through the point M (2, -3, 4) perpendicular to the line ..... and .....