Find the point at which the line given by the parametric equations below intersects the plane.
$$2 x + 4 y - 3 z = - 48 ; x = 10 + 7 t , \quad y = - 10 , z = 7 t$$
Select the correct answer.
A) $( 38 , - 10 , - 28 )$
B) $( - 43 , - 10,18 )$
C) $( - 38 , - 10,28 )$
D) $( 43 , - 10 , - 18 )$
E) $( 38 , - 10,28 )$

Question

Quizplus · Accepted Answer

Substitute $x = 10 + 7t$, $y = -10$, and $z = 7t$ into the plane equation $2x + 4y - 3z = -48$ and solve for $t$. Then, substitute $t$ back into the parametric equations to find the intersection point.

Find the Point at Which the Line Given by the Parametric