Plane Through a Given Point Parallel to a Given Line

Plane Through a Given Point Parallel to a Given Line

If the plane contains a line with direction vector:

$$\vec d$$

then its normal vector $$\vec n$$ must satisfy:

$$\vec n\cdot\vec d=0$$

For a plane through point $$P(x_1,y_1,z_1)$$:

$$\vec n\cdot(\vec r-\vec p)=0$$

Usage

- Used to construct a plane passing through a point and parallel to a specified line.