- #1

thepopasmurf

- 76

- 0

## Homework Statement

The greek letters look like they're superscripted, they're not supposed to be.

**a**,

**b**,

**c**are vectors

given that

[tex]\lambda[/tex]

**a**+ [tex]\mu[/tex]

**b**+ [tex]\nu[/tex]

**c**=

**0**

show that the points [tex]\alpha[/tex]

**a**, [tex]\beta[/tex]

**b**and [tex]\gamma[/tex]

**c**are collinear if

[tex]\lambda[/tex]/[tex]\alpha[/tex] + [tex]\mu[/tex]/[tex]\beta[/tex] + [tex]\nu[/tex]/[tex]\gamma[/tex] = 0

## Homework Equations

There are a lot of potentially relevant equations. Most important:

lines are collinear if

**a**= x

**b**

## The Attempt at a Solution

My attempt is really long so I won't post it here, I'll just outline my method.

I found the line between [tex]\alpha[/tex]

**a**and [tex]\beta[/tex]

**b**and said it was equal to x times the line between [tex]\beta[/tex]

**b**and [tex]\gamma[/tex]

**c**.

I also found

**a**in terms of

**b**and

**c**from

[tex]\lambda[/tex]

**a**+[tex]\mu[/tex]

**b**+ [tex]\nu[/tex]

**c**=

**0**

and subbed it into the former equation. However I got stuck because I had an x that I couldn't get rid of.