# Conversions between vectors

1. Jan 20, 2014

### Jhenrique

Given a vector $d\vec{r}=dx\hat{x}+dy\hat{y}+dz\hat{z}$ and another in its generalized form $d\vec{q}=h_1dq_1\hat{q_1}+h_2dq_2\hat{q_2}+h_3dq_3\hat{q_3}$, being that dr = dq. How I do for connect the informations of one with another?

The coordinates I know how do:
$$\\d\vec{r}=\frac{d\vec{r}}{d\vec{q}}d\vec{q} \\ \begin{bmatrix} dx\\ dy\\ \end{bmatrix} = \begin{bmatrix} \frac{\mathrm{d} x}{\mathrm{d} q_1} & \frac{\mathrm{d} x}{\mathrm{d} q_2}\\ \frac{\mathrm{d} y}{\mathrm{d} q_1} & \frac{\mathrm{d} y}{\mathrm{d} q_2}\\ \end{bmatrix} \begin{bmatrix} dq_1\\ dq_2\\ \end{bmatrix}$$

But, I don't know how convert the basis and scale factor. Someone could explain me?