How can I find the equation of a line perpendicular to a plane in 3D?

[Cpt Qwark]

Homework Statement

How would I find the equation of a line which passes through A(x₁, y₁, z₁) and is perpendicular to A(x₁, y₁, z₁) B(x₂, y₂, z₂), C(x₃, y₃, z₃)

Homework Equations

Cartesian form of a line in $$\mathbb{R}^3$$

The Attempt at a Solution

Not sure if this is right but would finding the equation of the plane which contains all three points and then finding the equation of the line that passes through A and that plane be correct?

 

[robphy]

Yes, but your line needs to be [as you say] perpendicular to the plane, which is equivalent to being parallel to the normal to the plane.

If you don't really care about the plane, you have enough information for find a normal-vector to the plane... by using cross-products.