Find the set of parametric equations of the line through the point $( - 3,6,3 ) \text { that is }$ parallel to the line $x = - 8 + 5 t , y = - 3 + 8 t$, and $z = 4 + 4 t$.
A) $x = - 3 - 5 t , y = 6 + 8 t , z = 3 - 4 t$
B) $x = - 3 - 8 t , z = 6 - 3 t , y = 3 + 4 t$
C) $x = - 3 + 5 t , y = - 6 + 8 t , z = 3 + 4 t$
D) $x = - 3 + 5 t , y = 6 + 8 t , z = 3 + 4 t$
E) $x = - 3 - 8 t , y = 6 - 3 t , z = 3 + 4 t$

Question

Find  the set of parametric equations of the line through the point $( - 3,6,3 ) \text { that is }$ parallel to the line $x = - 8 + 5 t , y = - 3 + 8 t$, and $z = 4 + 4 t$.
A) $x = - 3 - 5 t , y = 6 + 8 t , z = 3 - 4 t$
B) $x = - 3 - 8 t , z = 6 - 3 t , y = 3 + 4 t$
C) $x = - 3 + 5 t , y = - 6 + 8 t , z = 3 + 4 t$
D) $x = - 3 + 5 t , y = 6 + 8 t , z = 3 + 4 t$
E) $x = - 3 - 8 t , y = 6 - 3 t , z = 3 + 4 t$

Quizplus · Accepted Answer

The direction vector of the line is given by the coefficients of $t$ in the original line's equations, which are $5, 8,$ and $4$ for $x, y,$ and $z$ respectively. The new line passes through $(-3,6,3)$ and has the same direction, so its parametric equations are $x = -3 + 5t, y = 6 + 8t, z = 3 + 4t$.

Find the Set of Parametric Equations of the Line (−3,6,3) that is ( - 3,6,3 ) \text { that is }(−3,6,3) that is

Find the Set of Parametric Equations of the Line $( - 3,6,3 ) \text { that is }$