Homework Help: Discrete Math Help Urgent Pls =)

1. Jan 5, 2005

eme_girl

How do you find the angle between the co-ordinate axis (i.e. the xz plane) and another plane in general?

2. Jan 5, 2005

learningphysics

Angle between two planes is the angle between the normals of the planes.

3. Jan 5, 2005

HallsofIvy

Expanding on what learningphysics said, if one plane is given by Ax+ By+ Cz= D and the other by ax+ by+cz= d, then the normal vectors are Ai+ Bj+ Ck and ai+ bj+ ck respectively. u.v= |u||v|cos(θ) so θ, the angle between the two vectors and the angle between the planes, is given by cos(θ)= u.v/(|u||v|).

In particular, the xz-plane has normal vector j. If the other plane is given by Ax+By+Cz= D, its normal vector is Ai+Bj+Ck. The dot product of those is simply B so the angle between the planes is given by $cos(\theta)= \frac{B}{\sqrt{A^2+B^2+C^2}}$.

Last edited by a moderator: Jan 5, 2005