Find the transformation matrix $R$ that describes a rotation by 120◦ about an axis from the origin through the point (1, 1, 1). The rotation is clockwise as you look down the axis toward the origin
I had found similar question in PSE already. But that doesn't answer my question, So I am going to write new one.
In Griffiths EM I found that $\bar A_i = \sum_{j,k}(\sum_{i}R_{ij}R_{ik})A_jA_k =\sum_j \bar R_{ij}\bar A_j$
I wonder how can I find R from the equation. From tensor, I wrote
$$\begin{pmatrix}R_{xx} & R_{xy} & R_{xz} \\ R_{yx} & R_{yy} & R_{yz} \\ R_{zx} & R_{zy} & R_{zz}\end{pmatrix}=R$$ So I wrote $$\begin{pmatrix}\bar A_x \\ \bar A_y \\ \bar A_z\end{pmatrix}=R\begin{pmatrix} A_x \\ A_y \\ A_z\end{pmatrix}$$
I was thinking that how can I find R from the equation either. At first, I was thinking to sent right basis vectors to left so they will be tranpose matrix. From my study of matrix, I remember we don't deal with equation like that.
So how can I find $R$?
