Thread: Show that the two planes are neither coincident, parallel, nor distinct?

1. Show that the two planes are neither coincident, parallel, nor distinct?

I have a question on my homework I don't really understand, and I was wondering if anyone could help me.

The question is:

Show that the two planes are neither coincident, parallel, nor distinct. Identify, geometrically, how the planes intersect and determine the angle between the two planes to the nearest degree.

x + 2y - 4z + 7 = 0
2x - 2y - 5z + 10 = 0

If anyone could help me out I'd really appreciate it! Thanks in advance!

2. Originally Posted by Random-Hero-

The question is:

Show that the two planes are neither coincident, parallel, nor distinct. Identify, geometrically, how the planes intersect and determine the angle between the two planes to the nearest degree.

x + 2y - 4z + 7 = 0
2x - 2y - 5z + 10 = 0
Two planes, if they intersect, intersect in a line.
An equation of a plane has the form
$\displaystyle n_x x + n_y y + n_z z = d$
where $\displaystyle \vec n = <n_x,n_y,n_z>$ is the normal vector to the plane.
It can be shown that the angle between two planes' normal vector equals the angle between the planes. You can use the dot product
$\displaystyle \vec n_1 \cdot \vec n_2 = |n_1||n_2|cos(\theta)$
I am not sure if you copied the question correctly, as the two planes have different normal vectors so they must be distinct.

hth

3. I think the "nor distinct" is really meant to say "parallel and distinct" I think its just a typo.