Chapter 11.5, Problem 13ES

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 $L_1\text{ and }{L}_2$ intersect at a point $\left(x,y,z\right),$ then there exists a single value of t such that $\begin{array}{l}{L}_0:x=x_0+a_{0}t,y=y_0+b_{0}t,z=z_0+c_{0}t\hfill \\ L_1:x=x_1+a_{1}t,y=y_1+b_{1}t,z=z_1+c_{1}t\hfill \end{array}$ are satisfied.