Reshebnik Arutyunov Yu N12 Setting Higher Mathematics

The finished solution. Reshebnik Arutyunov. Task №12.

11-20. Given the coordinates of the vertices of the pyramid A1A2A3A4:
Find: 1) the length of the edges A1A2; 2) the angle between the edges A1A2 and A1A4; 3) the angle between the edge and the edge A1A4 A1A2A3; 4) area of the face A1A2A3; 5) The volume of the pyramid; 6) The equation of the line A1A2; 7) the equation A1A2A3 plane; 8) the equation of height is lowered from the top of the A4 to the brink A1A2A3. Make a drawing.

12. A1 (4; 4; 10), A2 (4; 10; 2), A3 (2; 8; 4), A4 (9, 6, 4)