Find two dots on a line that is determined by plane cross:
$5x + 3y – 1 = 0$
$2x + 3z + 5 = 0$
That are the same length from two planes $3x + 3y – 2 = 0$ and $4x + y + z + 4 = 0$.
I found a line equation:
$x = -1 + 3t$
$y = 2 – 5t$
$z = -1 – 2t$
Now I don't know how to find two dots that are the same length from those two planes.
My another question is how it is possible that there are two dots on a line that is the same distance from two planes. I thought there is only one.
Best Answer
Points that are equidistant from a pair of non-parallel planes lie on their two angle bisectors, which are themselves planes. Work out their equations and then find the intersection of the given line with the bisectors.