Answer:
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
Step-by-step explanation:
Step(i):-
Given point P = ( 4,2,4)
Given vector is -2 i - 5 j - 3 k
The vector equation of a line through the point a⁻ and parallel to b⁻ is
r⁻ = a⁻ + t b⁻
Given r⁻ = 4 i + 2 j + 4 k
r⁻ = 4 i + 2 j + 4 k + t (-2 i - 5 j - 3 k)
Step(ii):-
The Cartesian form
[tex]\frac{x-a_{1} }{b_{1} } = \frac{y-a_{2} }{b_{2} } = \frac{z-a_{3} }{b_{3} } = t[/tex]
[tex]\frac{x-4 }{-2 } = \frac{y-2 }{-5 } = \frac{z-4 }{-3 } = t[/tex]
[tex]\frac{x-4 }{-2 } = t[/tex]
⇒ x - 4 = -2 t
⇒ x = - 2 t + 4
[tex]\frac{y-2 }{-5 } = t[/tex]
⇒ y - 2 = - 5 t
⇒ y = - 5 t + 2
[tex]\frac{z-4 }{-3 } = t[/tex]
z - 4 = -3 t
z = - 3 t + 4
Conclusion:-
The parametric equations are
x = - 2 t + 4 , y = - 5 t + 2 , z = - 3 t + 4
