Find a set of symmetric equations for the line through the point and parallel to the specified vector or line.
Point: $( - 7,0,2 )$ Parallel to: $\mathbf { v } = 4 \mathbf { i } + 5 \mathbf { j } - 3 \mathbf { k }$
A)Symmetric equations: $\frac { x + 7 } { - 3 } = \frac { y } { 5 } = \frac { z - 2 } { 4 }$
B)Symmetric equations: $\frac { x + 7 } { 4 } = \frac { y } { 5 } = \frac { z - 2 } { - 3 }$
C)Symmetric equations: $\frac { x + 7 } { 4 } = \frac { z } { 5 } = \frac { y - 2 } { - 3 }$
D)Symmetric equations: $\frac { x + 5 } { 4 } = \frac { y } { 5 } = \frac { z - 2 } { - 3 }$
E)Symmetric equations: $\frac { x + 7 } { 4 } = \frac { y + 7 } { 5 } = \frac { z - 2 } { - 3 }$

Question

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line.
Point: $( - 7,0,2 )$ Parallel to: $\mathbf { v } = 4 \mathbf { i } + 5 \mathbf { j } - 3 \mathbf { k }$ 
A)Symmetric equations: $\frac { x + 7 } { - 3 } = \frac { y } { 5 } = \frac { z - 2 } { 4 }$
B)Symmetric equations: $\frac { x + 7 } { 4 } = \frac { y } { 5 } = \frac { z - 2 } { - 3 }$
C)Symmetric equations: $\frac { x + 7 } { 4 } = \frac { z } { 5 } = \frac { y - 2 } { - 3 }$
D)Symmetric equations: $\frac { x + 5 } { 4 } = \frac { y } { 5 } = \frac { z - 2 } { - 3 }$
E)Symmetric equations: $\frac { x + 7 } { 4 } = \frac { y + 7 } { 5 } = \frac { z - 2 } { - 3 }$

Quizplus · Accepted Answer

The symmetric equations of a line can be found using the formula $\frac{x-x_0}{a} = \frac{y-y_0}{b} = \frac{z-z_0}{c}$, where $(x_0, y_0, z_0)$ is a point on the line and $a, b, c$ are the direction ratios from the vector parallel to the line. Given point $(-7, 0, 2)$ and vector $4\mathbf{i} + 5\mathbf{j} - 3\mathbf{k}$, the correct symmetric equations are $\frac{x + 7}{4} = \frac{y}{5} = \frac{z - 2}{-3}$.

Find a Set of Symmetric Equations for the Line Through (−7,0,2)( - 7,0,2 )(−7,0,2)

Find a Set of Symmetric Equations for the Line Through $( - 7,0,2 )$