Function of distance between a point and vector in 3D

[Rosengrip]

Homework Statement

Two lines are given p: [tex]\stackrel{\rightarrow}{r}[/tex](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 [tex]\stackrel{\rightarrow}{r}[/tex](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 [tex]\sqrt{m}[/tex]

Homework Equations

An equation for a distance between a vector and point

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

e = direction vector of p
r[tex]_{0}[/tex] = position vector of p
r[tex]_{1}[/tex] = 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.

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]

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

Use Maple if this is a lot of work