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

Answer 1

The equation of a line passing through (xo, yo, zo) and normal to the plane {(x, y, z): ax + by + cz = d} can be found by taking the normal vector of the plane and using it as the direction vector of the line.

The normal vector of the plane is given by (a, b, c).

So, the equation of the line is:
x = xo + at
y = yo + bt
z = zo + ct

where t is a parameter.

This line is parallel to the plane and perpendicular to its normal vector.