Equation of a Line Through a Point and Parallel to a Vector

Equation of a Line Through a Point and Parallel to a Vector

For point $$P(x_1,y_1,z_1)$$ and direction vector:

$$\vec d=a\hat i+b\hat j+c\hat k$$

the line is:

$$\vec r=(x_1\hat i+y_1\hat j+z_1\hat k)+\lambda(a\hat i+b\hat j+c\hat k)$$

Usage

- Used to construct a line from one point and its direction.