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: (0,0,0)
Parallel to: $\mathbf { v } = ( 5,6,7 )$
A)Parametric equations: $x = 6 t , y = 5 t , z = 7 t$
B)Parametric equations: $x = 5 t , y = 6 t , z = 7 t$
C)Parametric equations: $x = 6 t , y = 7 t , z = 5 t$
D)Parametric equations: $x = 7 t , y = 6 t , z = 5 t$
E)Parametric equations: $x = 7 t , y = 6 t , z = 7 t$

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: (0,0,0)
Parallel to: $\mathbf { v } = ( 5,6,7 )$ 
A)Parametric equations: $x = 6 t , y = 5 t , z = 7 t$
B)Parametric equations: $x = 5 t , y = 6 t , z = 7 t$
C)Parametric equations: $x = 6 t , y = 7 t , z = 5 t$
D)Parametric equations: $x = 7 t , y = 6 t , z = 5 t$
E)Parametric equations: $x = 7 t , y = 6 t , z = 7 t$

Quizplus · Accepted Answer

The correct parametric equations for a line through the origin (0,0,0) and parallel to the vector $\mathbf{v} = (5,6,7)$ are $x = 5t, y = 6t, z = 7t$, as they directly use the components of the vector $\mathbf{v}$ as direction numbers.

Find a Set of Parametric Equations for the Line Through v=(5,6,7)\mathbf { v } = ( 5,6,7 )v=(5,6,7)

Find a Set of Parametric Equations for the Line Through $\mathbf { v } = ( 5,6,7 )$