Function of distance between a point and vector in 3D

[Rosengrip]

1. The problem statement, all variables and given/known data

Two lines are given p: \stackrel{\rightarrow}{r}(t) = (4,7,4) + t(2,2,-8) and q: z = 3, x = 7 -y (second one is given in parametric form).

Questions:
a)
find a function f(x) which has a value in x that equals a distance from a point \stackrel{\rightarrow}{r}(x) (which lies on the first line, e.g. p) to line q squared (squared refers to the whole function).

b)
find minimum m of function f(x) and analyze the meaning of \sqrt{m}
2. Relevant equations
An equation for a distance between a vector and point

d = http://www.shrani.si/f/z/nX/128JEovx/distance.jpg

e = direction vector of p
r_{0} = position vector of p
r_{1} = vector from point to one of the points defining a line

Equations for converting from vector to parametric form, which are really simple and I won't be writing here.



3. The attempt at a solution

Now I only have basic knowledge about vectors only and I was learning them some time ago. I can guess this assignment is pretty simple but because we haven't done any similar cases at the course, I don't really know where to begin.

Any hint would be greatly appreciated.

[Outlined]

rewrite the other one to a param. equation (with a variable t') as well
compute the distance D = || point on line 1 - point on line 2 ||
We want to know for which t and t' the distance D is minimal
To make it easy this is the same as looking at how D2 is minimal
now you found your t and t' you can compute (by the param. eqn.) the two points
compute the distance between the two points


Use Maple if this is a lot of work