(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

a,b,care 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]band [tex]\gamma[/tex]care collinear if

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

2. Relevant equations

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

lines are collinear ifa= xb

3. 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]aand [tex]\beta[/tex]band said it was equal to x times the line between [tex]\beta[/tex]band [tex]\gamma[/tex]c.

I also foundain terms ofbandcfrom

[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.

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# Vector Problem

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