Shown in the explanation
Position vector of a particle at a given instant is given by:
[tex]\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}[/tex]
On the other hand, the average velocity is the change in the particle’s position vector divided by time interval:
[tex]\vec{v}=\frac{\Delta \vec{r}}{\Delta t}=\frac{\vec{r_{2}}-\vec{r_{1}} }{t_{2}-t_{1}} \\ \\ \\ Where: \\ \\ \\ \vec{r_{1}}: Initial \ position \\ \\ \vec{r_{2}}: Final \ position \\ \\ t_{1}:Initial \ time \\ \\ t_{2}:Final \ time[/tex]
So we have:
[tex]\vec{r_{1}}=7\hat{i}+7\hat{j}+1\hat{k} \\ \\ \vec{r_{2}}=7\hat{i}+7\hat{j}+8\hat{k} \\ \\ \\ Then: \\ \\ \Delta \vec{r} = \vec{r_{2}}-\vec{r_{1}}=7\hat{i}+7\hat{j}+8\hat{k}-(7\hat{i}+7\hat{j}+1\hat{k}) \\ \\ \Delta \vec{r}=7\hat{k} \\ \\ \\ We \ also \ know: \\ \\ \Delta t=5s[/tex]
Finally, the average velocity is:
[tex]\vec{v}=\frac{\Delta \vec{r}}{\Delta t} \\ \\ \\ \vec{v}=\frac{7\hat{k}}{5} \\ \\ \boxed{\vec{v}=\frac{7}{5}\hat{k} \ units/s}[/tex]
