Find a set of symmetric equations for the line through the point and parallel to the specified vector or line.
Point: (7,0,0)
Parallel to: $\mathbf { v } = ( 5,6,7 )$
A)Symmetric equations: $\frac { x } { 5 } = \frac { y } { 7 } = \frac { z - 7 } { 7 }$
B)Symmetric equations: $\frac { x } { 7 } = \frac { y } { 6 } = \frac { z } { 5 }$
C)Symmetric equations: $\frac { x - 7 } { 5 } = \frac { y } { 6 } = \frac { z } { 7 }$
D)Symmetric equations: $\frac { x } { 5 } = \frac { y - 7 } { 5 } = \frac { z } { 7 }$
E)Symmetric equations: $\frac { x - 7 } { 6 } = \frac { y } { 5 } = \frac { z } { 7 }$

Question

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. 
Point: (7,0,0)
Parallel to: $\mathbf { v } = ( 5,6,7 )$ 
A)Symmetric equations: $\frac { x } { 5 } = \frac { y } { 7 } = \frac { z - 7 } { 7 }$
B)Symmetric equations: $\frac { x } { 7 } = \frac { y } { 6 } = \frac { z } { 5 }$
C)Symmetric equations: $\frac { x - 7 } { 5 } = \frac { y } { 6 } = \frac { z } { 7 }$
D)Symmetric equations: $\frac { x } { 5 } = \frac { y - 7 } { 5 } = \frac { z } { 7 }$
E)Symmetric equations: $\frac { x - 7 } { 6 } = \frac { y } { 5 } = \frac { z } { 7 }$

Quizplus · Accepted Answer

The symmetric equations for a line can be written as $\frac{x-x_0}{a} = \frac{y-y_0}{b} = \frac{z-z_0}{c}$, where $(x_0, y_0, z_0)$ is a point on the line and $(a, b, c)$ is a direction vector parallel to the line. Given the point (7,0,0) and the direction vector $(5,6,7)$, the correct symmetric equations are $\frac{x-7}{5} = \frac{y}{6} = \frac{z}{7}$.

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

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