Chapter 11.4, Problem 46E

To determine

To find: A set of parametric equation of the lines passing through given point and parallel to the specified vector.

Answer to Problem 46E

  $x=-1+5t,y=4-t,z=-3$

Explanation of Solution

Given information:

A line is passing through point $(-1,4,-3)$ and is parallel to $\text{v}=5i-j$ .

Concepts used:

Vectors are used for determining equation of a line in space. A line passing through the point $P(x_1,y_1,z_1)$ and parallel to the vector $\text{v}=\langle a,b,c\rangle$ is represented by the Parametric equations-

  $x=x_1+at,y=y_1+bt,z=z_1+ct$ ;where, $a,b,c$ are direction numbers of vector $\text{v}=\langle a,b,c\rangle$ .

Calculation:

Line is passing through the point $(-1,4,-3)$ .

So, $x_1=-1,y_1=4,z_1=-3$ .

Line is parallel to the direction vector $\text{v}=5i-j$ .

So, direction numbers are $a=5,b=0,c=-1$ .

Now parametric equation of the lines passing through point $(-1,4,-3)$ and is parallel to $\text{v}=5i-j$ will be given as-

  $\begin{array}{l}x=x_1+at,y=y_1+bt,z=z_1+ct\\ \Rightarrow x=-1+5t,y=4-t,z=-3+0t\\ \Rightarrow x=-1+5t,y=4-t,z=-3\end{array}$

Hence, desired parametric equation of line is $x=-1+5t,y=4-t,z=-3$ .