# How to find the shortest distance between two lines ? (1 Viewer)

#### SB257426

##### Member
The question basically is:

Find the shortest distance between lines r = i+2j+3k + lambda (2i+j+4k) and r = 2i+4j+5k + mu (3i+4j+5k).

I don't get these sort of questions and I really need help. Can someone give me a solution that doesn't involve the use of matrices please.

#### SB257426

##### Member
The question basically is:

Find the shortest distance between lines r = i+2j+3k + lambda (2i+j+4k) and r = 2i+4j+5k + mu (3i+4j+5k).

I don't get these sort of questions and I really need help. Can someone give me a solution that doesn't involve the use of matrices please.

#### cossine

##### Well-Known Member
The question basically is:

Find the shortest distance between lines r = i+2j+3k + lambda (2i+j+4k) and r = 2i+4j+5k + mu (3i+4j+5k).

I don't get these sort of questions and I really need help. Can someone give me a solution that doesn't involve the use of matrices please.
So how come you don't want a solution involving matrices. Matrices are very important.

#### carrotsss

##### New Member
So how come you don't want a solution involving matrices. Matrices are very important.
Matrices aren’t in the HSC syllabus, and if you want to achieve your best in the HSC the most time efficient way to do so is to stay within the syllabus, even if matrices are very important knowledge they can wait

• Masaken

#### ExtremelyBoredUser

##### Bored Uni Student
The question basically is:

Find the shortest distance between lines r = i+2j+3k + lambda (2i+j+4k) and r = 2i+4j+5k + mu (3i+4j+5k).

I don't get these sort of questions and I really need help. Can someone give me a solution that doesn't involve the use of matrices please.
The solution is pretty trivial (I hate this word but gotta use it let this be the exception) if you have a geometric conceptualisation of projections. I highly suggest you watch videos on projections in the 2D/3D space and see how they deduce the distance.

These are one of the questions which if you just grind through and learn algebraically its gonna be futile if they throw some words out but if you can visualise this and have that intuition, its basically free marks.

• Masaken

#### synthesisFR

##### Well-Known Member
shortest distance u do vector projection (unless u are given the foot of the normal and they want the distance to that)