Option 30 DHS 3.1

Option 30 DHS 3.1

№1.30. Given the four points A1 (0; 4; 5); A2 (3; –2; 1); A3 (4; 5; 6); A4 (3; 3; 2). Make equations: a plane A1A2A3; b) straight A1A2; c) straight A4M, perpendicular to the A1A2A3 plane; d) straight A3N parallel to straight line A1A2; e) a plane passing through the point A4, perpendicular to the straight line 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.
№2.30. Determine at what value of the C plane 3x - 5y + Cz - 3 = 0; and x - 3y + 2z + 5 = 0 will be perpendicular.
№ 3.30. Find a point symmetric to the point M (4; 3; 10) with respect to a straight line ....