If I know vectors B and r, and want to find vector m, knowing that all 3 vectors are coplanar, and m makes an angle $\theta$ with r, how do I find m?
I know that m $\cdot$ B x r = 0, and m $\cdot$ r = cos($\theta$), so I guess I need to solve simultaneously m $\cdot$ n =0 and m $\cdot$ r = cos($\theta$), where n = B x r. But how do I do this?
From the condition that the vectors are coplanar we obtain for some $x,y\in \mathbb{R}$
$$\vec m=x\, \vec B+y\,\vec r$$
and from the other condition
$$\vec m \cdot \vec r=x\, \vec B\cdot \vec r+y\,\vec r \cdot \vec r=|\vec m|\cdot|\vec r|\cdot\cos \theta$$
we need some other extra condition to find $x$ and $y$.