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trasher [3.6K]
3 years ago
5

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).
Mathematics
1 answer:
tia_tia [17]3 years ago
7 0

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

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