Question

How would I find the shortest distance between two lines if the lines are in vector form? Do I first put it in parametric form?

Answer 1

cross them to define a normal and the planes between them is one thought

then all you have to do is find the distance between the planes

Answer 2

spose we have the points (x1, y1, z1) on line 1 and (x2, y2, z2) on line 2

and the direction vectors cross to get (a,b,c)

the planes are just:

a(x-x1) + b(y-y1) + c(z-z1) = 0

and

a(x-x2) + b(y-y2) + c(z-z2) = 0

and the line that stabs between them is some

x = x1 + at
y = y1 + bt
z = z1 + ct

insert them into each plane to define 2 points that you can then find the distance between.

its not the formula i know but i can never remember the formula

Answer 3

another idea is after you have the planes .... and a line between them

Answer 4

|n| |L| cos(a) = n.L

cos(a) = n.L/|n| |L|

|L| cos(a) = n.L/|n|

Answer 5

id go that route, seems simpler lol

Answer 6

ok thanks!