Question

Find a line through (xo, yo, zo) and normal to the plane {(x, y, z): ax + by + cz = d}

Answer 1

A line through (xo, yo, zo) can be represented as:

x = xo + at
y = yo + bt
z = zo + ct

where a, b, and c are direction ratios of the line, and t is a parameter.

Now, we need to find a line that is normal to the plane {(x, y, z): ax + by + cz = d}. A normal vector to the plane can be represented as (a, b, c).

So, a line through (xo, yo, zo) and normal to the plane is:

x = xo + at
y = yo + bt
z = zo + ct

This line will be perpendicular to the plane as the direction ratios (a, b, c) of the line are the same as the normal vector of the plane.