Respuesta :
Answer:
B) x = -4t - 1; y = 8t - 1; z = 4t - 1
Step-by-step explanation:
Explanation:-
Given points are P(-1,-1,-1) and Q(-5,7,3)
Let (x₁ , y₁ , z₁) = P(-1,-1,-1)
Let (x₂ , y₂ , z₂) = Q(-5,7,3)
Parametric equation of the line passing through the points (x₁ , y₁ , z₁) and (x₂ , y₂ , z₂)
[tex]\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} } = \frac{z-z_{1} }{z_{2}-z_{1} } = t[/tex]
[tex]\frac{x-(-1)}{-5-(-1)} = \frac{y -(-1)}{7-(-1)} = \frac{z-(-1)}{3-(-1)} = t[/tex]
[tex]\frac{x-(-1)}{-4} = \frac{y -(-1)}{8} = \frac{z-(-1)}{4} = t[/tex]
Equating each term
[tex]\frac{x+1}{-4} = t[/tex]
⇒ x + 1 = - 4 t
⇒ x = - 4 t -1
[tex]\frac{y +1}{8} = t[/tex]
y + 1 = 8 t
⇒ y = 8 t - 1
[tex]\frac{Z+1}{4} =1[/tex]
⇒ z +1 = 4t
⇒ z = 4t -1
Final answer:-
parametric equations for the line through point P(-1,-1,-1) and Q(-5,7,3)
are
x = -4t - 1; y = 8t - 1; z = 4t - 1
