# If the planes #x=cy+bz# , #y=cx+az# , #z=bx+ay# go through the straight line, then is it true that #a^2+b^2+c^2+2abc=1#?

##### 1 Answer

Mar 9, 2017

Yes, it is true. Please see below for details.

#### Explanation:

Let the planes

As the planes pass through line

Similarly

Solving them for

which implies

and substituting in third we get

or

or