How Can Vector C Be Expressed in Terms of A, B, and u?

[thenewbosco]

Hello, my problem is as follows:

Given that A and B are known vectors, and
$$A \cdot C=u$$ is a known quantity, and $$A \times C=B$$
Express C in terms of A,B, u, and the magnitude of A

So far what i have done was use the definition of the dot product as AC cos $$\theta$$=u, and cross product as AC sin $$\theta$$=|B|, squared both and added them to get an expression for the magnitude of C squared, however i do not know how to get the vector C by itself in terms of the quantities in the question, can anyone explain how i should go about this? thanks

 

[daveb]

I would recommend using the vector triple product and determine Ax(AxC) = AxB, expanding out the left side