Distance between a point and a line and between two lines 
Let $P = (-5, 3, 4)$, $Q = (-6, 0, 3)$, $R = (-7, 1, 6)$ and $S = (-4, 2, 2)$. Let $A$ be the line passing through $P$ and $Q$, and let $B$ be the line passing through $R$ and $S$.
a) What is the distance between $R$ and $A$?
b) What is the distance between $A$ and $B$?

I am quite confused on how to start with this problem. Firstly, I am not entirely sure how I will find the distance between the point and the line. Would that distance simply be the normal vector multiplied by the projection? If so, how exactly would I calculate the projection here? No equations for the lines are given so I am quite confused.
Also, for the shortest distance between two lines, will it be a similar approach of finding the normal vector and projection?
I am not entirely sure how to proceed here. Any help would be highly appreciated!

Let P = (-5, 3, 4), Q = (-6, 0, 3), R = (-7, 1, 6) and S = (-4, 2, 2). Let A be the line passing through P and Q, and let B be the line passing through R and S.
a)What is the distance between R and A?
parametrise A  to  get $$x=-5-t,y=3-3t,z=4-t$$
The distance is minimized when $$D^2 =(t-2)^2+(3t-2)^2+(t+2)^2$$ is minimized.
Upon differentiation and solving for t, you find the minimum distance between R and A.   
b) What is the distance between A and B?
parametrise B  to  get $$x=-7+3s,y=1+s,z=6-4s$$
The distance is minimized when 
$$ D^2= (-5-t+7-3s)^2 +(3-3t-1-s)^2+(4-t-6+4s)^2 $$ is minimized.
Differentiate with respect to t and s.
Solve for t and s to find the minimum distance.
