Find a set of symmetric equations of the line that passes through the points $( 3,0,3 )$ and $( 7,4 , - 2 )$.
A) $\frac { x } { 7 } = \frac { y } { 4 } = \frac { z } { - 2 }$
B) $\frac { x - 3 } { 4 } = \frac { y - 4 } { 4 } = \frac { z - 2 } { - 5 }$
C) $\frac { x - 3 } { - 4 } = \frac { y } { 4 } = \frac { z - 3 } { 5 }$
D) $\frac { x + 4 } { 3 } = y - 4 = \frac { z - 5 } { 3 }$
E) $\frac { x - 3 } { 4 } = \frac { y } { 4 } = \frac { z - 3 } { - 5 }$

Question

Quizplus · Accepted Answer

To find the symmetric equations of the line passing through points $ (3,0,3) $ and $ (7,4,-2) $, first find the direction vector by subtracting the coordinates of the first point from the second: $ \vec{d} = (7-3, 4-0, -2-3) = (4, 4, -5) $. The symmetric equations of the line are given by $ \frac{x-x_1}{d_x} = \frac{y-y_1}{d_y} = \frac{z-z_1}{d_z} $, where $ (x_1, y_1, z_1) $ is a point on the line (e.g., $ (3,0,3) $) and $ (d_x, d_y, d_z) $ are the components of the direction vector. Substituting the values, we get $ \frac{x-3}{4} = \frac{y-0}{4} = \frac{z-3}{-5} $, which matches choice E.

Find a Set of Symmetric Equations of the Line That (3,0,3)( 3,0,3 )(3,0,3)

Find a Set of Symmetric Equations of the Line That $( 3,0,3 )$