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
[tex]P_L = Vt + A[/tex]
Where t, is a real number, and [tex]P_L[/tex] 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:
[tex]P_L = (0,0,1) t + (-4, 0.5, 5)[/tex]
The equations for each coordinate are:
[tex]x = -4\\y = 0.5\\z = 5 + t[/tex]
