Question

What can be said about two lines that are perpendicular to the same plane?

Answer 1

They are parallel.

Explanation:

If the equation of the plane is written `ax+by+cz+d = 0` then any line perpendicular to it can be written in parametric form as:

`l(t) = (x_0, y_0, z_0) + t(a, b, c)`

where `(x_0, y_0, z_0)` is any point through which the line passes.

Any two such lines will be parallel.

Answer 2

Two lines perpendicular to the same plane are parallel.

Explanation:

From plane geometry:
if two lines cross a third line in such a manner that the sum of the interior angles is `180^@` then the lines are parallel.

If two lines are perpendicular to the same plane then a line through the two points of intersection with the plane will form a `90^@` with each of the original two lines.