Find a set of parametric equations for the line through the point and parallel to the specified vector or line.(For each line,write the direction numbers as integers. )
Point: $( 2,0,2 )$ Parallel to: $x = 3 + 4 t , y = 5 - 5 t , z = - 7 + 3 t$
A)Parametric equations: $x = 4 t , y = - 5 t , z = 2 + 3 t$
B)Parametric equations: $x = 2 + 4 t , y = 2 - 5 t , z = 2 + 3 t$
C)Parametric equations: $x = 2 + 4 t , y = - 5 t , z = 2 + 3 t$
D)Parametric equations: $x = 2 + 4 t , y = 2 - 5 t , z = 2 - 2 t$
E)Parametric equations: $x = 2 + - 5 t , y = 3 t , z = 2 + 4 t$

Question

Find a set of parametric equations for the line through the point and parallel to the specified vector or line.(For each line,write the direction numbers as integers. ) 
Point: $( 2,0,2 )$ Parallel to: $x = 3 + 4 t , y = 5 - 5 t , z = - 7 + 3 t$ 
A)Parametric equations: $x = 4 t , y = - 5 t , z = 2 + 3 t$
B)Parametric equations: $x = 2 + 4 t , y = 2 - 5 t , z = 2 + 3 t$
C)Parametric equations: $x = 2 + 4 t , y = - 5 t , z = 2 + 3 t$
D)Parametric equations: $x = 2 + 4 t , y = 2 - 5 t , z = 2 - 2 t$
E)Parametric equations: $x = 2 + - 5 t , y = 3 t , z = 2 + 4 t$

Quizplus · Accepted Answer

The direction numbers of the given line are $4, -5, 3$. So, the parametric equations of the line through the point $(2, 0, 2)$ and parallel to the given line are:$$x = 2 + 4t, \quad y = 0 - 5t, \quad z = 2 + 3t$$

Find a Set of Parametric Equations for the Line Through (2,0,2)( 2,0,2 )(2,0,2)

Find a Set of Parametric Equations for the Line Through $( 2,0,2 )$