Question

Find an equation for a plane that contains the x–axis and makes an angle
of pi/3 with the plane x+y+z = 0.

Answer 1

\[cos(\frac{pi}{3})=\frac{<1,1,1>\cdot <x,0,z>}{|<1,1,1>|~|x,0,z|}\]

Answer 2

musn't it be <0,x,z> and not (x,0,z)? because the x axis has the form <x,0,0>

Answer 3

the normals should be pi/3 in order for the planes to be pi/3

any normal that includes the x axis will be confined within the zy plane

so yeah, <0,y,z> looks better :)

Answer 4

relatively speaking that is