dist between parallel lines in 3d

how do we find the distance between parallel lines

6 Answers

62
Lokesh Verma ·

Let the first lne be

r-a=λm (where r, a, m are vectors)
2nd line be
r-b=λm
So The answer is as simple as distance of a point on the 1st line to the 2nd line!

so u can simply find the distance of a from the line r-b=λm

or alternatively b from r-a=λm

1
coolpal ·

u can find d distance of 1 line frm origin.
tthen find d dist of 2nd line frm origin
result:subtract d distances and u get d in b/w dist

i find it simple as common sense is reqd.

hope u find it easy 2.

62
Lokesh Verma ·

No cool.. ur answre will not work!

Think again!

1
varun ·

It will work only if the two lines are in the same side of the origin right ?

62
Lokesh Verma ·

No not even then!
It will work only if both lines lie on the same plane as the origin!

See this one.. will it work here?
The same side of origin logic will not work! can u see what i am saying?

1
coolpal ·

yup i agree .my ans .is confined 2 only if pts lie on same plane.my method can only b applied if2 pts lie on same side of origin.
thanx a lot 4 correcting me.

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