Chapter 11.5, Problem 14ES

Determine whether the statement is true or false. Explain your answer. In these exercises $L_0\text{and}{L}_1$ are lines in 3-space whose parametric equations are

$\begin{array}{l}{L}_0:x=x_0+a_{0}t,y=y_0+b_{0}t,z=z_0+c_{0}t\hfill \\ L_1:x=x_1+a_{1}t,y=y_1+b_{1}t,z=z_1+c_{1}t\hfill \end{array}$

If $L_0$ passes through the origin, then the vectors $〈a_0,b_0,c_0〉\text{ and }〈x_0,y_0,z_0〉$ are parallel.