Problem5:Find the formula for the angle between a line and a plane and use it to find the angle (in degrees) between the plane x+y-z = -1 and the line y = 1 - 3x on the xy-plane. |
SOLUTION:
| The angle between a line and a plane is, |
> Ang := (v,n) -> convert(Pi/2 - angle(v,n),degrees);
Ang := (v, n) -> convert(1/2 Pi - angle(v, n), degrees)
| let's test it, |
> Ang([1,0,0],[-1,1,0]);
-45 degrees
| so it does work... don't worry about the sign. Now let us apply it to the line and plane in the problem. |
> Ang([1,-3,0],[1,1,-1]);
1/2 1/2
(- 1/2 Pi + arccos(1/15 10 3 )) degrees
180 --------------------------------------------
Pi
| relax! |
> evalf(%);
-21.41671405 degrees