Find parametric equations for the line described below.
-The line through the point P(5, -7, -4) and parallel to the line x = 5t - 4, y = 3t - 1, z = 2t + 3
A) x = 3t + 5, y = -5t, z = -4
B) x = 5t + 5, y = 3t - 7, z = 2t - 4
C) x = 5, y = 2t - 7, z = -3t - 4
D) x = 5t - 5, y =3t + 7, z = 2t + 4

Question

Quizplus · Accepted Answer

Since the line we are trying to find is parallel to the given line, the direction vectors of both lines are the same. The direction vector of the given line is <5, 3, 2>. Therefore, the direction vector of our line is also <5, 3, 2>. Now, we need to find the parametric equations for the line passing through point P(5, -7, -4) with direction vector <5, 3, 2>. Using the point-direction form of the equation of a line, we get: x = 5t + 5 y = 3t - 7 z = 2t - 4 Therefore, the best choice is B.

Find Parametric Equations for the Line Described Below