Find a set of parametric equations of the line.
Passes through $( - 7,4,7 )$ and is perpendicular to $- x + 4 y + z = 5$ .

A) $\begin{array} { l }
x = - 7 - 7 t \
y = 4 - 4 t \
z = 7 + t
\end{array}$
B) $\begin{array} { l }
x = - 7 - 7 t \
y = 4 - 4 t \
z = 7 - t
\end{array}$
C) $\begin{array} { l }
x = - 7 - 7 t \
y = 4 + 4 t \
z = 7 - t
\end{array}$
D) $\begin{array} { l }
x = - 7 - 7 t \
y = 4 + 4 t \
z = 7 + t
\end{array}$
E) $\begin{array} { l }
x = - 7 + 7 t \
y = 4 + 4 t \
z = 7 + t
\end{array}$

Question

Find a set of parametric equations of the line. 
Passes through $( - 7,4,7 )$ and is perpendicular to $- x + 4 y + z = 5$ .
 
A) $\begin{array} { l } 
x = - 7 - 7 t \
y = 4 - 4 t \
z = 7 + t
\end{array}$  
B) $\begin{array} { l } 
x = - 7 - 7 t \
y = 4 - 4 t \
z = 7 - t
\end{array}$  
C) $\begin{array} { l } 
x = - 7 - 7 t \
y = 4 + 4 t \
z = 7 - t
\end{array}$  
D) $\begin{array} { l } 
x = - 7 - 7 t \
y = 4 + 4 t \
z = 7 + t
\end{array}$  
E) $\begin{array} { l } 
x = - 7 + 7 t \
y = 4 + 4 t \
z = 7 + t
\end{array}$

Quizplus · Accepted Answer

The line is perpendicular to the plane $-x + 4y + z = 5$, so its direction vector is $(-1, 4, 1)$. The parametric equations using point $(-7, 4, 7)$ and direction vector $(-1, 4, 1)$ are $x = -7 - t$, $y = 4 + 4t$, $z = 7 + t$, which matches option D.

Find a Set of Parametric Equations of the Line (−7,4,7)( - 7,4,7 )(−7,4,7)

Find a Set of Parametric Equations of the Line $( - 7,4,7 )$