Find the parametric form for the equation of the line that goes through the points $$ A=(1,-1,5) $$ and $$ B=(-4,-3,7) $$. Use the point $$ A $$ and the vector $$ A B $$. $$ \begin{array}{ll}x=\text { Ex: } 6+8 \mathrm{t} & \text { Enter as: } a+b t \text { or } a-b t \ y=\square \ z=\square\end{array} $$

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Given the two points
$$
A = (1,-1,5) \quad \text{and} \quad B = (-4,-3,7),
$$
the direction vector $$ \vec{AB} $$ is calculated as:
$$
\vec{AB} = B - A = (-4-1,\,-3-(-1),\,7-5) = (-5,\, -2,\, 2).
$$

Using point $$ A $$ and the direction vector $$ \vec{AB} $$, the parametric equations for the line are:
$$
\begin{aligned}
x &= 1 - 5t, \
y &= -1 - 2t, \
z &= 5 + 2t.
\end{aligned}
$$
The parametric equations for the line are: $$ \begin{aligned} x &= 1 - 5t, \ y &= -1 - 2t, \ z &= 5 + 2t. \end{aligned} $$

Find the parametric form for the equation of the line that goes through the points
and . Use the point and the vector .

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Find the parametric form for the equation of the line that goes through the points and . Use the point and the vector .