Find a set of symmetric equations for the line through the point and parallel to the specified vector or line.
Point: $( - 2,2,0 )$ Parallel to: $\mathbf { v } = \frac { 3 } { 7 } \mathrm { i } - \frac { 4 } { 7 } \mathbf { j } - 3 \mathrm { k }$
A)Symmetric equations: $\frac { x } { 3 } = \frac { y - 2 } { - 21 } = \frac { z } { - 4 }$
B)Symmetric equations: $\frac { x + 2 } { 3 } = \frac { y - 2 } { 3 } = \frac { z } { - 21 }$
C)Symmetric equations: $\frac { x + 2 } { 3 } = \frac { y - 2 } { - 4 } = \frac { z - 6 } { - 3 }$
D)Symmetric equations: $\frac { x + 2 } { 3 } = \frac { y - 2 } { - 4 } = \frac { z } { - 21 }$
E)Symmetric equations: $\frac { x + 2 } { - 4 } = \frac { y } { 3 } = \frac { z } { - 21 }$

Question

Find a set of symmetric equations for the line through the point and parallel to the specified vector or line. 
Point: $( - 2,2,0 )$ Parallel to: $\mathbf { v } = \frac { 3 } { 7 } \mathrm { i } - \frac { 4 } { 7 } \mathbf { j } - 3 \mathrm { k }$ 
A)Symmetric equations: $\frac { x } { 3 } = \frac { y - 2 } { - 21 } = \frac { z } { - 4 }$
B)Symmetric equations: $\frac { x + 2 } { 3 } = \frac { y - 2 } { 3 } = \frac { z } { - 21 }$
C)Symmetric equations: $\frac { x + 2 } { 3 } = \frac { y - 2 } { - 4 } = \frac { z - 6 } { - 3 }$
D)Symmetric equations: $\frac { x + 2 } { 3 } = \frac { y - 2 } { - 4 } = \frac { z } { - 21 }$
E)Symmetric equations: $\frac { x + 2 } { - 4 } = \frac { y } { 3 } = \frac { z } { - 21 }$

Quizplus · Accepted Answer

The symmetric equations of a line can be written as $\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}$, where $(x_1, y_1, z_1)$ is a point on the line and $a, b, c$ are the direction ratios of the line, which are the components of the parallel vector. Given the point $(-2, 2, 0)$ and the vector $\frac{3}{7}\mathbf{i} - \frac{4}{7}\mathbf{j} - 3\mathbf{k}$, the direction ratios are $3, -4, -21$ (multiplying the vector components by 7 to clear the fraction). Thus, the correct symmetric equations are $\frac{x + 2}{3} = \frac{y - 2}{-4} = \frac{z}{-21}$.

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

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