Cartesian Form from Vector Form

Cartesian Form from Vector Form

From:

$$\vec r=\vec a+\lambda\vec d$$

with:

$$\vec a=x_1\hat i+y_1\hat j+z_1\hat k$$

and:

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

the Cartesian form is:

$$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$$

Usage

- Used to convert a vector equation of a line into Cartesian form.