# Intersecting planes

• Aug 25th 2011, 07:19 AM
Veronica1999
Intersecting planes
1. The planes -x+2y+3z=4 and 2x+3y-z=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 x-1 / 1 = y-2 / -5/11 = z-1 / 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+3y-z=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.... ?
• Aug 25th 2011, 10:33 AM
Siron
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:
$\displaystyle \theta=\arccos\left(\frac{x_1\cdot x_2+y_1\cdot y_2+z_1\cdot z_2}{\sqrt{x_1^2+y_1^2+z_1^2}+\sqrt{x_2^2+y_2^2+z_ 2^2}}\right)$
• Aug 27th 2011, 09:19 AM
Veronica1999
Re: Intersecting planes
Thank You.