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Fifthman
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Homework Statement
Consider the equation [itex]$\mathbf{A}\mathbf{\times Y}=$\mathbf{B}$ [/itex] for perpendicular vectors A and B.
Derive a general solution for Y.
Homework Equations
The solution was actually given to us, and I plugged it into make sure it works. (It does.)
[itex]
\textbf{$\mathbf{Y=\frac{1}{\left|A\right|^{2}}}(c\mathbf{A}-\mathbf{A\times}\mathbf{B})$}
[/itex]
The Attempt at a Solution
The solution, conceptually, is the set of all vectors Y perpendicular to B such that
[itex]
$\left|\mathbf{Y}\right|sin\theta=\mathbf{\frac{|B|}{|A|}}$
[/itex]
As an aside, I tried taking
[itex]
\mathbf{A}\mathbf{\times(A\times B})=\mathbf{A(A}\cdot\mathbf{B)}-\mathbf{B|A|^{2}}
[/itex]
noting that A and B are perpendicular.
The instructor, as a hint, suggested solving the system:
[itex]
$\mathbf{A}\mathbf{\times Y}=$\mathbf{B}$
[/itex]
[itex]
$\mathbf{A}\mathbf{\times Y_{o}}=$\mathbf{B}$
[/itex]
which gave me
[itex]
$\mathbf{A}\mathbf{\times(Y-Y_{o})}=$\mathbf{0}$
[/itex]
What am I missing that could help me tie this together?
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