Find a set of parametric equations of the line that passes through the given points. $( 5,0,6 ) , ( 1,6 , - 3 )$
A) $x = 5 - 4 t , y = 6 t , z = - 9 t$
B) $x = 5 - 4 t , y = 5 + 6 t , z = 6 - 9 t$
C) $x = 5 - 4 t , y = 6 t , z = 6 - 9 t$
D) $x = 6 - 4 t , y = 1 - 6 t , z = 6 - 9 t$
E) $x = 6 - 4 t , y = 6 t , z = 5 - 9 t$

Question

Find a set of parametric equations of the line that passes through the given points.  $( 5,0,6 ) , ( 1,6 , - 3 )$ 
A) $x = 5 - 4 t , y = 6 t , z = - 9 t$
B) $x = 5 - 4 t , y = 5 + 6 t , z = 6 - 9 t$
C) $x = 5 - 4 t , y = 6 t , z = 6 - 9 t$
D) $x = 6 - 4 t , y = 1 - 6 t , z = 6 - 9 t$
E) $x = 6 - 4 t , y = 6 t , z = 5 - 9 t$

Quizplus · Accepted Answer

To find the parametric equations of the line through points $ (5,0,6) $ and $ (1,6,-3) $, we first find the direction vector by subtracting the coordinates of the first point from the second, resulting in $ \langle 1-5, 6-0, -3-6 \rangle = \langle -4, 6, -9 \rangle $. Then, using one of the points as the base (e.g., $ (5,0,6) $), the parametric equations are $ x = 5 - 4t $, $ y = 6t $, $ z = 6 - 9t $.

Find a Set of Parametric Equations of the Line That (5,0,6),(1,6,−3)( 5,0,6 ) , ( 1,6 , - 3 )(5,0,6),(1,6,−3)

Find a Set of Parametric Equations of the Line That $( 5,0,6 ) , ( 1,6 , - 3 )$