Answer: x = -4, y = 0.5, z = 5 +t
Hi!
The line L whose direction is parallel to vector V a passes through point A
is parametrized
![P_L = Vt + A](https://tex.z-dn.net/?f=P_L%20%3D%20Vt%20%2B%20A)
Where t, is a real number, and
is a any point on line L.
In this case the direction is that of the z-axis , so V = (0, 0, 1)
A is the midpoint between points B = (0, -4, 9) and C=(-8, 5, 1)
The midpoint is A = (B + C)/2 = (-4, 0.5, 5)
Then the line is:
![P_L = (0,0,1) t + (-4, 0.5, 5)](https://tex.z-dn.net/?f=P_L%20%3D%20%280%2C0%2C1%29%20t%20%2B%20%28-4%2C%200.5%2C%205%29)
The equations for each coordinate are:
![x = -4\\y = 0.5\\z = 5 + t](https://tex.z-dn.net/?f=x%20%3D%20-4%5C%5Cy%20%3D%200.5%5C%5Cz%20%3D%205%20%2B%20t)