Ryabushko A.P. IDZ 3.1 option 17

№1.17. Given four points A1 (6; 6; 5); A2 (4; 9; 5); A3 (4; 6; 11); A4 (6; 9; 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 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;
№2.17. Find the equation of the plane passing through the point M(1,-1,2) perpendicular to the segment M1M2; If M1 (2;3; 4); M2(-1, 2, -3).
№3.17. Show that the straight line parallel to the plane x + 3y - 2z + 1 = 0; and the line x = t + 7; y = t - 2; z = 2t + 1 lies in that plane.