Find parametric equations for the line described below.
-The line through the points P(-1, -1, 7) and Q( -7, 4, 3)
A) x = -6t - 1, y = 5t - 1, z = -4t + 7
B) x = t - 6, y = t + 5, z = 7t - 4
C) x = t + 6, y = t - 5, z = 7t + 4
D) x = -6t + 1, y = 5t + 1, z = -4t - 7

Question

Quizplus · Accepted Answer

To find the parametric equations of a line through points P and Q, we first find the direction vector $\vec{PQ} = Q - P = (-7 - (-1), 4 - (-1), 3 - 7) = (-6, 5, -4)$. Then, using point P as the reference, the parametric equations are $x = -1 - 6t$, $y = -1 + 5t$, and $z = 7 - 4t$, which simplifies to $x = -6t - 1$, $y = 5t - 1$, $z = -4t + 7$.

Find Parametric Equations for the Line Described Below