Find a set of parametric equations of the line that passes through the given points. $( 2,3,0 ) , ( 9,9,12 )$
A) $x = 2 - 7 t , y = 3 + 6 t , z = 12 t$
B) $x = 2 + 7 t , y = 3 + 6 t , z = 12 t$
C) $x = 2 + 7 t , y = 3 - 6 t , z = - 12 t$
D) $x = 2 - 7 t , y = 3 - 6 t , z = - 12 t$
E) $x = 2 + 6 t , y = 3 + 7 t , z = 12 t$

Question

Find a set of parametric equations of the line that passes through the given points.  $( 2,3,0 ) , ( 9,9,12 )$ 
A) $x = 2 - 7 t , y = 3 + 6 t , z = 12 t$
B) $x = 2 + 7 t , y = 3 + 6 t , z = 12 t$
C) $x = 2 + 7 t , y = 3 - 6 t , z = - 12 t$
D) $x = 2 - 7 t , y = 3 - 6 t , z = - 12 t$
E) $x = 2 + 6 t , y = 3 + 7 t , z = 12 t$

Quizplus · Accepted Answer

To find the parametric equations of the line passing through points $ (2,3,0) $ and $ (9,9,12) $, we calculate the direction vector by subtracting the coordinates of the first point from the second: $ \Delta x = 9 - 2 = 7 $, $ \Delta y = 9 - 3 = 6 $, and $ \Delta z = 12 - 0 = 12 $. Thus, the parametric equations are $ x = 2 + 7t $, $ y = 3 + 6t $, and $ z = 12t $, which matches option B.

Find a Set of Parametric Equations of the Line That (2,3,0),(9,9,12)( 2,3,0 ) , ( 9,9,12 )(2,3,0),(9,9,12)

Find a Set of Parametric Equations of the Line That $( 2,3,0 ) , ( 9,9,12 )$