Chapter 11.5, Problem 42ES

Sketch the vectors ${\text{r}}_0=〈2,0,4〉{\text{ and r}}_{\text{1}}=〈0,4,0〉,$ and then sketch the vectors $\frac{1}{4}{\text{r}}_0,\frac{3}{4}{\text{r}}_1,\frac{1}{2}{\text{r}}_0+\frac{1}{2}{\text{r}}_1,\frac{3}{4}{\text{r}}_0+\frac{1}{4}{\text{r}}_1$ Draw the line segment $\left(1-t\right){\text{r}}_0+t{\text{r}}_{\text{1}}\left(0\le t\le 1\right).$ If n is a positive integer, what is the position of the point on this line segment corresponding to $t=1/n,$ relative to the points $\left(2,0,4\right)\text{ and }\left(0,4,0\right)?$