Find parametric equations for the line through the point $( 5,6,3 )$ that is parallel to the plane $x + y + z = - 15$ and perpendicular to the line $x = 15 + t , y = 12 - t , z = 3 t$.
Select the correct answer.
A) $\quad x = 4 t + 5 , y = - 2 t + 6 , z = - 2 t + 3$
B) $x = 4 t , y = - 2 t + 6 , z = - 2 t$
C) $x = 4 t + 2 , y = - 2 t + 6 , z = - 2 t + 3$
D) $x = 4 t + 2 , y = - 2 t + 6 , z = 0$
E) $x = 4 t , y = - 2 t , z = - 2 t + 3$

Question

Quizplus · Accepted Answer

The direction vector of the line must be perpendicular to the normal vector of the plane $(1, 1, 1)$ and parallel to the direction vector of the given line $(1, -1, 3)$. The cross product of these vectors gives $(4, -2, -2)$, which is the direction vector for the required line. Using the point $(5, 6, 3)$, the parametric equations are $x = 4t + 5$, $y = -2t + 6$, $z = -2t + 3$.

Find Parametric Equations for the Line Through the Point (5,6,3)( 5,6,3 )(5,6,3)

Find Parametric Equations for the Line Through the Point $( 5,6,3 )$