A(1,2,k) lies on the plane x + 2y - 2z = 8. Find:
a) the value of k.
b) the coordinates of B such that AB is normal to the plane and 6 units from it.
The part b) is a good bit more difficult.
We need to find a value of $\displaystyle t$ so that $\displaystyle \overrightarrow {AB} = t\left\langle {1,2, - 2} \right\rangle \;\& \,\left\| {t\left\langle {1,2, - 2} \right\rangle } \right\| = 6$
Note there are two such points for $\displaystyle B$.