- #1

spacetimedude

- 88

- 1

## Homework Statement

A line is inclined at equal angles to the x-, y-, z- axes and passes through the origin. Another line passes through the points (1,2,4) and (0,0,1). Find the minimum distance between the two lines.

## Homework Equations

d=|(r2-r1).n(hat)|

## The Attempt at a Solution

r1=i+j+k

r2=i+2j+4k

n=(i+j+k)x(i+2j+4k)=2i-3j+k

|n|=1/[itex]\sqrt{14}[/itex]

d=(1/14)|k.(2i-3j+k)|=1/[itex]\sqrt{14}[/itex]

The answer says that the r2=k+λ(i+2j+3k) and the final answer is 1/[itex]\sqrt{6}[/itex].

Could you care to explain why r2=k+λ(i+2j+3k) and when finding n, the answer excludes the lone k in r2=k+λ(i+2j+3k)? Also, when doing these kind of problems, does it matter if d=|(r1-r2).n(hat)| and not d=|(r2-r1).n(hat)|? I'm having difficulties trying to figure out which vector to subtract first.

Thank you