The parametric equations of the line through (3,2,1) in the direction of $3 \mathbf { i } - \mathbf { j } + \mathbf { k }$ is

A) $x = 3 t + 3 , y = t + 2 , z = t + 1$
B) $x = 3 t + 3 , y = - t + 2 , z = t + 1$
C) $x = 3 t - 3 , y = - t + 2 , z = t + 1$
D) $x = 3 t + 3 , y = - t + 2 , z = t - 1$
E) $x = 3 t - 3 , y = t + 2 , z = t - 1$

Question

The parametric equations of the line through (3,2,1) in the direction of $3 \mathbf { i } - \mathbf { j } + \mathbf { k }$ is

A) $x = 3 t + 3 , y = t + 2 , z = t + 1$
B) $x = 3 t + 3 , y = - t + 2 , z = t + 1$
C) $x = 3 t - 3 , y = - t + 2 , z = t + 1$
D) $x = 3 t + 3 , y = - t + 2 , z = t - 1$
E) $x = 3 t - 3 , y = t + 2 , z = t - 1$

Quizplus · Accepted Answer

The direction vector given is $3 \mathbf { i } - \mathbf { j } + \mathbf { k }$, which translates to changes in $x$, $y$, and $z$ as $3t$, $-t$, and $t$ respectively. Starting from the point $(3,2,1)$, the parametric equations become $x = 3t + 3$, $y = -t + 2$, and $z = t + 1$.

The Parametric Equations of the Line Through (3,2,1) in the Direction