Chapter 11.5, Problem 52ES

Let L be the line that passes through the point $\left(x_0,y_0,z_0\right)$ and is parallel to the vector $\text{v}=〈a,b,c〉,$ where a, b, and c are nonzero. Show that a point $\left(x,y,z\right)$ lies on the line L if and only if $\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{z-z_0}{c}$ These equations, which are called the symmetric equations of L, provide a nonparametric representation of L.