QPaperGen

Let \(\vec{p}\), \(\vec{q}\), and \(\vec{r}\) be the position vectors of points P, Q, and R, respectively.

The vector from Q to P is found by subtracting the position vector of the tail (Q) from the position vector of the head (P):\[\vec{QP} = \vec{p} - \vec{q} = \vec{\alpha} - \vec{\beta}\]

Given that \[\vec{QR} = \frac{3}{2} \vec{QP}\]
Substitute the expression for \(\vec{QP}\):\[\vec{QR} = \frac{3}{2} (\vec{\alpha} - \vec{\beta})\]
\[\vec{r} = \vec{\beta} + \frac{3}{2} (\vec{\alpha} - \vec{\beta})\]
\[\vec{r} = \frac{3}{2} \vec{\alpha} + \left(1 - \frac{3}{2}\right) \vec{\beta}\]
The position vector of the point R is:$\(\vec{r} = \frac{3}{2} \vec{\alpha} - \frac{1}{2} \vec{\beta}\)$