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

i) Find all vectorsvsuch that <1,2,1> Xv= <3,1,-5>

ii) Explain why there is no vectorvsuch that <1,2,1> Xv= <3,1,5>

2. Relevant equations

aXb= <a[itex]_{2}[/itex]b[itex]_{3}[/itex] - a[itex]_{3}[/itex]b[itex]_{2}[/itex], a[itex]_{3}[/itex]b[itex]_{1}[/itex] - a[itex]_{1}[/itex]b[itex]_{3}[/itex], a[itex]_{1}[/itex]b[itex]_{2}[/itex] - a[itex]_{2}[/itex]b[itex]_{1}[/itex])

3. The attempt at a solution

i)

<1,2,1> Xv

= <2v[itex]_{3}[/itex] -v[itex]_{2}[/itex], v[itex]_{1}[/itex] - v[itex]_{3}[/itex], v[itex]_{2}[/itex] - 2v[itex]_{1}[/itex]>

Which leaves me with three equations:

2v[itex]_{3}[/itex] -v[itex]_{2}[/itex] = 3

v[itex]_{1}[/itex] - v[itex]_{3}[/itex] = 1

v[itex]_{2}[/itex] - 2v[itex]_{1}[/itex] = -5

Now, every time I try to fiddle with them, I end up with 0 = 0.

Any help?

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# Cross Product problem

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