Chapter 10.4, Problem 65E

To determine

To find: The error in writing symmetric equations of the line that passes through $\left(1,2,6\right)$ and parallel to $v=\langle 3,5,4\rangle$ .

  $\frac{x-3}{1}=\frac{y-5}{2}=\frac{z-4}{6}$

Answer to Problem 65E

The error in the equation $\frac{x-3}{1}=\frac{y-5}{2}=\frac{z-4}{6}$ is that direction numbers was taken as passing points and passing points were taken as direction numbers.

Explanation of Solution

Given information:

The equation of line passes through $\left(1,2,6\right)$ and parallel to $v=\langle 3,5,4\rangle$ .

Calculation:

The general form of symmetric line is $\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$ .

Substitute $1$ , $2$ , $6$ for $x_1$ , $y_1$ , $z_1$ and $3$ , $5$ , $4$ for $a$ , $b$ , $c$ in the general equation.

  $\begin{array}{c}\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}\\ \frac{x-1}{3}=\frac{y-2}{5}=\frac{z-6}{4}\end{array}$

So, the correct symmetric equations of the line that passes through $\left(1,2,6\right)$ and parallel to $v=\langle 3,5,4\rangle$ is $\frac{x-1}{3}=\frac{y-2}{5}=\frac{z-6}{4}$ .

Therefore, the error in the equation $\frac{x-3}{1}=\frac{y-5}{2}=\frac{z-4}{6}$ is that direction numbers was taken as passing points and passing points were taken as direction numbers.