- #1

Krushnaraj Pandya

Gold Member

- 697

- 73

## Homework Statement

how to write the vector equation of the line of shortest distance between two skew lines in the shortest and most efficient way?

(The exact lines given in a particular problem in my book can be referenced- L1=(3i+8j+3k)+λ(3i-j+k) and L2=(-3i-7j+6k)+μ(-3i+2j+4k) )

**2. Relevant methods**

The vector we want would be perpendicular to both the lines, so we can use dot product=0 for both lines which gives us 2 equations in l,m and n where vector=li+mj+nk. We can find distance between the lines from a routine formula then equate the modulus of the vector sqrt(l^2+m^2+n^2) to that distance

## The Attempt at a Solution

combined above