Find the locus of the point which moves so that its distance
from the line x=y=z is twice its distance from the plane x + y+z=1.
I know the distance of point (x,y,z) from given plane will be mod(x+y+z-1)/3^(1/2).How to find distance that from given line?I tried to find distance of (0,0,0) and (x,y,z) and then taking its component along normal to line, but failed.
Best Answer
Here is a geometrical proof (see Fig. below)
This question is easy to tackle when you consider what happens in a section plane passing through line (D) (with equation $x=y=z$) : the locus is clearly a pair of half lines passing through point $A$ (with 3D coordinates $(0,0,1)$).
Revolving this 2D locus around line (D) gives the 3D locus : a half cone with axis (D), apex $A$ and aperture angle $\arctan 2$.