1. Lines and Planes Help!

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.

2. Well a) according to me would be (assuming in the place of k there should the z axis coordinate, so then z=k) 1 + 2*2 - 2z = 8 => 1 + 4 - 2z = 8 => 2z = 5 - 8 => 2z = -3 /:2 => z = -1.5

3. The part b) is a good bit more difficult.

We need to find a value of $t$ so that $\overrightarrow {AB} = t\left\langle {1,2, - 2} \right\rangle \;\& \,\left\| {t\left\langle {1,2, - 2} \right\rangle } \right\| = 6$

Note there are two such points for $B$.