## 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. |

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