
Intersecting planes
1. The planes x+2y+3z=4 and 2x+3yz=4 intersect to form a line. Find an equation for the line.
I found two points that satisfy both equations.
(1,1,1) (2, 6/11, 18/11)
The equation is x1 / 1 = y2 / 5/11 = z1 / 7/11
Is it correct?
2. To the nearest tenth of a degree, find the size of the acute dihedral angle formed by the intersecting planes. Hmmm....
I have an approach but I am not sure if it will work.
The perpendicular vector of the plane x+2y +3z = 4 is
(1, 2, 3) and the perpendicular vector for the plane 2x+3yz=4 is (2, 3, 1)
cos(x) = 1/14
x=85.9
I think I read somewhere that you use the dot product of the perpendicular vectors
of a plane to get the dihedral angle.... ?

Re: Intersecting planes
They're both fine! And yes the angle $\displaystyle \theta$ between two planes with normal vectors $\displaystyle (x_1,y_1,z_1)$ and $\displaystyle (x_2,y_2,z_2)$ can be calculated as:
$\displaystyle \theta=\arccos\left(\frac{x_1\cdot x_2+y_1\cdot y_2+z_1\cdot z_2}{\sqrt{x_1^2+y_1^2+z_1^2}+\sqrt{x_2^2+y_2^2+z_ 2^2}}\right)$

Re: Intersecting planes