Chapter 9.6, Problem 5E

To determine

To find: The parametric equation for the line passes through the given point and parallel to given vector.

Answer to Problem 5E

The parametric equation for the line passes through the given point and parallel to given vectoris $x=3,y=2-4t,z=1+2t$ .

Explanation of Solution

Given information:

The points and vector are $P\left(3,2,1\right),v=\langle 0,-4,2\rangle$ .

Calculation:

The parametric equation is given as,

  $\begin{array}{l}x=x_0+ta\\ y=y_0+tb\\ z=z_0+tc\end{array}$

Substitute the values in above equation.

  $\begin{array}{l}x=3+0t\\ x=3\\ y=2-4t\\ z=1+2t\end{array}$