# Find the parametric equation for the line through (5,1,0) that is perpendicular to the plane 2x - y + z = 1.

Find the parametric equation for the line through (5,1,0) that is perpendicular to the plane 2x - y + z = 1.
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Coleman Ali
r(t)=<5,1,0>+<2,-1,1>t
In parametric form
x=2t+5
y=1-t
z=t
We are looking for when this line intersects the coordinateplanes.. In other word, we want to know where the line passesthrough the planes x = 0, y = 0, and z = 0. Starting with the intersection point for the plane z =0. We knowthat the plane z =0 contains all points where the z coordinate is 0... Hence the z coordinate on our line must also be 0 when it intersects. Setting z = 0
t=0
Using t=0, in the parametric equations for x and y, we find the x and y coordinates of the intersection.
x=5
y=1
(5,1,0)
Following the same procedure for the plane y = 0, by setting y=0
0=1-t
t=1
x=7
z=1
(7,0,1)
And for x = 0
$t=-\frac{5}{2}$
$y=\frac{7}{2}$
$z=-\frac{5}{2}$
$\left(0,\frac{7}{2},-\frac{5}{2}\right)$