Question

Find parametric equations for the line through point P(-1,-1,-1) and Q(-5,7,3) A. x = t + 4; y = t - 8; z = -1t - 4

Answer 1

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)

$\frac{x-x_{1} }{x_{2}-x_{1} } = \frac{y-y_{1} }{y_{2}-y_{1} } = \frac{z-z_{1} }{z_{2}-z_{1} } = t$

$\frac{x-(-1)}{-5-(-1)} = \frac{y -(-1)}{7-(-1)} = \frac{z-(-1)}{3-(-1)} = t$

$\frac{x-(-1)}{-4} = \frac{y -(-1)}{8} = \frac{z-(-1)}{4} = t$

Equating  each term

             $\frac{x+1}{-4} = t$

     ⇒  x + 1 = - 4 t

    ⇒   x = - 4 t -1

          $\frac{y +1}{8} = t$  

         y + 1 = 8 t

     ⇒  y  = 8 t - 1

        $\frac{Z+1}{4} =1$

  ⇒  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