Find a set of parametric equations of the line.
Passes through $( - 1,6 , - 3 )$ and is parallel to $\mathbf { v } = 5 \mathbf { i } - \mathbf { j }$ .

A) $\begin{array} { l }
x = - 1 + 5 t \
y = 6 - t \
z = 3
\end{array}$
B) $\begin{array} { l }
x = - 1 + 5 t \
y = - 6 - t \
z = - 3
\end{array}$
C) $\begin{array} { l }
x = 1 + 5 t \
y = 6 - t \
z = 3
\end{array}$
D) $\begin{array} { l }
x = - 1 + 5 t \
y = 6 - t \
z = - 3
\end{array}$
E) $\begin{array} { l }
x = 1 + 5 t \
y = 6 - t \
z = - 3
\end{array}$

Question

Find a set of parametric equations of the line. 
Passes through $( - 1,6 , - 3 )$ and is parallel to $\mathbf { v } = 5 \mathbf { i } - \mathbf { j }$ .

A) $\begin{array} { l } 
x = - 1 + 5 t \
y = 6 - t \
z = 3
\end{array}$
B) $\begin{array} { l } 
x = - 1 + 5 t \
y = - 6 - t \
z = - 3
\end{array}$
C) $\begin{array} { l } 
x = 1 + 5 t \
y = 6 - t \
z = 3
\end{array}$
D) $\begin{array} { l } 
x = - 1 + 5 t \
y = 6 - t \
z = - 3
\end{array}$
E) $\begin{array} { l } 
x = 1 + 5 t \
y = 6 - t \
z = - 3
\end{array}$

Quizplus · Accepted Answer

The parametric equations of a line passing through a point $(x_0, y_0, z_0)$ and parallel to a vector $\mathbf{v} = ai + bj + ck$ are $x = x_0 + at$, $y = y_0 + bt$, $z = z_0 + ct$. Here, the line passes through $(-1, 6, -3)$ and is parallel to $\mathbf{v} = 5\mathbf{i} - \mathbf{j}$, so the equations are $x = -1 + 5t$, $y = 6 - t$, $z = -3$.

Find a Set of Parametric Equations of the Line (−1,6,−3)( - 1,6 , - 3 )(−1,6,−3)

Find a Set of Parametric Equations of the Line $( - 1,6 , - 3 )$