(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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Dot Product/Cross Product Interpretation, Geometric Construction

**Physics Forums | Science Articles, Homework Help, Discussion**