Find parametric equations for the line that passes through the point P and is parallel to the vector v. $P ( 0,0,0 ) , \quad \mathrm { v } = \langle - 5,2,9 \rangle$
A) $x = - 5 t , y = 2 t , z = 9 t$
B) $x = 5 - 5 t , y = 2 + 2 t , z = 9 - 9 t$
C) $x = 2 - 5 t , y = - 5 + 2 t , z = 9 t$
D) $x = - 5 , y = 2 , z = 9$
E) none of these

Question

Quizplus · Accepted Answer

A line parallel to the given vector can be parameterized as $P+t\mathbf{v}$. Substituting $P=(0,0,0)$ and $\mathbf{v}=(-5,2,9)$, we get $x=-5t$, $y=2t$, and $z=9t$. Thus, the answer is choice A.

Find Parametric Equations for the Line That Passes Through the Point