How to Find \vec{b} in a Cross Product Problem?

AI Thread Summary
To find vector \vec{b} in the equation \vec{a} X \vec{b} = \vec{c}, one must recognize that multiple vectors can satisfy this condition, all lying in the plane perpendicular to \vec{c}. The key is to find a vector that is perpendicular to both \vec{a} and \vec{c}, which can be achieved using the cross product. The relationship \vec{a} X \vec{c} = \vec{b} can be utilized to derive \vec{b}. Understanding the geometric interpretation of cross products is essential for solving this problem effectively. This approach allows for the identification of suitable vectors \vec{b} that meet the criteria.
FrankJ777
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I have a question about solving a problem involving a cross product. I understand how to find \vec{a} X \vec{b} = \vec{c}, but if \vec{a} and \vec{c} are given how do I find \vec{b}? Is there something I can do analogous to c/a =b? I've been reviewing my old calc III and linear algebra notes, but I havn't been able to figure it out. Any help would be most appreciated.

Thanks
 
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Given a and c, there are several possible vectors b such that a x b = c. They all lie in the plane perpendicular to c.
 
do you know how to find a vector that is perpendicular to another vector?
 
a x c = b

since b is a vector that is perpendicular to both a and c .. :-D
 

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