At student demonstrations yesterday we were solving this task:
"Find the equation of the plane parallel to the plane $x - 2y + 2z - 5 = 0$ and distanced 2 units from the plane."
We read the normal from the equation, which is $\vec n = (1, -2 ,2)$. The length of $\vec n$ is $9$, so we conclude that $\vec n$ is not of unit length. We get that $\vec n_0 = (\frac 13, - \frac 23, \frac 23)$.
Now here's the part that I don't understand:
The demonstrator wrote this equation:
$\frac 13 |\delta| = 2$
and from that we get that $\delta = 6$.
I'm not seeing how he reached this conslusion that led him to write $\frac 13 |\delta| = 2$. Isn't $\delta$ supposed to be the distance from the origin? Can someone clarify?
Thanks in advance!