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Line in Plane Equation

The line parameterized by \[\mathbf{v} = \begin{pmatrix} 1 + t \\ 3t \\ 1 - t \end{pmatrix}\]lies in a plane of the form $ x + y + cz = d $. Enter the ordered pair $ (c,d) $.

1
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+
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-
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$\frac{a}{b}$
.
0
=
%

$a^n$
$a^{\circ}$
$a_n$
$\sqrt{}$
$\sqrt[n]{}$
$\pi$
$\ln{}$
$\log$
$\theta$
$\sin{}$
$\cos{}$
$\tan{}$

$($
$)$
$[$
$]$
$\cap$
$\cup$
$,$
$\infty$