Answer
$\begin{bmatrix}Q\vec{r}_{1}&\cdots&Q\vec{r}_{p}\end{bmatrix}=QR$, where $R=\begin{bmatrix}\vec{r}_{1}&\cdots&\vec{r}_{p}\end{bmatrix}$.
Work Step by Step
This is simply the definition of the matrix product, where we are given the columns of $R$ instead of the matrix $R$ itself. Note that $Q$ is $m\times n$ and $R$ is $n\times p$, so $QR$ is an $m\times p$ matrix.
