Find parametric equations for the line described below. -The line through the point $\mathrm { P } ( - 5 , - 4,4 )$ in the direction of the vector $$ A) $x = - 8 t + 5 , y = 6 t + 4 , z = - 6 t - 4$ B) $x = - 8 t - 5 , y = - 6 t - 4 , z = 6 t + 4$ C) $x = 8 t - 5 , y = - 6 t - 4 , z = - 6 t + 4$ D) $x = 8 t + 5 , y = - 6 t + 4 , z = - 6 t - 4$

Question

Find parametric equations for the line described below.
-The line through the point $\mathrm { P } ( - 5 , - 4,4 )$ in the direction of the vector $< 8 , - 6 , - 6 >$
A) $x = - 8 t + 5 , y = 6 t + 4 , z = - 6 t - 4$
B) $x = - 8 t - 5 , y = - 6 t - 4 , z = 6 t + 4$
C) $x = 8 t - 5 , y = - 6 t - 4 , z = - 6 t + 4$
D) $x = 8 t + 5 , y = - 6 t + 4 , z = - 6 t - 4$

Quizplus · Accepted Answer

The parametric equations for a line can be found using the formula $x = x_0 + at$, $y = y_0 + bt$, and $z = z_0 + ct$, where $(x_0, y_0, z_0)$ is a point on the line and $$ is the direction vector. For the given point $P(-5, -4, 4)$ and direction vector $<8, -6, -6>$, the correct parametric equations are $x = -5 + 8t$, $y = -4 - 6t$, and $z = 4 - 6t$, which matches choice C.

Find Parametric Equations for the Line Described Below P(−5,−4,4)\mathrm { P } ( - 5 , - 4,4 )P(−5,−4,4)

Find Parametric Equations for the Line Described Below $\mathrm { P } ( - 5 , - 4,4 )$