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

Given the nonzero vectoraε ℝ^{3},a[itex]\dot{}[/itex]x= b ε ℝ, anda×x=cε ℝ^{3}, can you determine the vectorxε ℝ^{3}? If so, give a geometric construction forx.

2. Relevant equations

a[itex]\dot{}[/itex]x= ||a||||x||cos[itex]\Theta[/itex]

3. The attempt at a solution

I'm not really certain what it is asking for?

Obviously, the cross product of the two vectors creates a vector perpendicular to all vectors in the a, x plane. And, the magnitude of the cross product defines the area of a parallelogram spanned by a and x.

Also, ||x||cos[itex]\Theta[/itex] is the length of the projection of x onto a, which is also equal to b/||a||

But while I know all this, I don't know what I'm trying to show or how to show it?

Any help would be great! Thanks!

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# Dot Product/Cross Product Interpretation, Geometric Construction

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