TITLE: Solution to Problem5
# !b1 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.

!b3 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


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