Question

Find equations of the line that is parallel to the z-axis and passes through the midpoint between the two points (0, −3, 7) and (−2, 4, 1).

Answer 1

Answer:

$\vec{r}(t)=\left$

In parametric form:

$x=-1, y=\displaystyle\frac{1}{2}, z=4+t$

Step-by-step explanation:

We first find the mid point:

$\displaystyle\left(\frac{0+(-2)}{2},\frac{-3+4}{2},\frac{7+1}{2}\right)=\left(-1,\frac{1}{2},4\right)$

Then, a vector parallel to the z-axis is:

$\vec{v}=\left< 0,0,1 \right>$

Then remember the equation of  a line passing through point $(x_o,y_o,z_o)$ and parallel to the vector $\vec{v}=\left$ is:

$\vec{r}(t)=\left+t\left$

So, in this problem we get:

$\vec{r}(t)=\left+t\left$

After combining the two vectors:

$\vec{r}(t)=\left$

In parametric form:

$x=-1, y=\displaystyle\frac{1}{2}, z=4+t$