Another service from Omega

Solution to Problem5


*****

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

Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>
Last modified: Mon Feb 7 16:11:26 EST 2000