The position vector M, N and R from the origin are m, n and r respectively. If R is a point on MN such that MR = 1/4 RN, find an expression for r in terms of m and n.

Here are the solutions to the remaining questions.

Q1) The position vector M, N and R from the origin are $\mathbf{m}$, $\mathbf{n}$ and $\mathbf{r}$ respectively. If R is a point on $\vec{MN}$ such that $\vec{MR} = \frac{1}{4}\vec{RN}$, find an expression for $\mathbf{r}$ in terms of $\mathbf{m}$ and $\mathbf{n}$.

Step 1: Express the vectors $\vec{MR}$ and $\vec{RN}$ in terms of their position vectors.

$$\vec{MR} = \mathbf{r} - \mathbf{m}$$ $$\vec{RN} = \mathbf{n} - \mathbf{r}$$

Step