Find a plane containing the line
{
x
(
t
)
=
−
6
−
7
t
y
(
t
)
=
7
+
3
t
z
(
t
)
=
−
1
+
8
t
\displaystyle {\left\lbrace\begin{array}{ccc} {x}{\left({t}\right)}&=&-{6}-{7}{t}\\{y}{\left({t}\right)}&=&{7}+{3}{t}\\{z}{\left({t}\right)}&=&-{1}+{8}{t}\end{array}\right.}
⎩
⎨
⎧
x
(
t
)
y
(
t
)
z
(
t
)
=
=
=
−
6
−
7
t
7
+
3
t
−
1
+
8
t
and orthogonal to the plane
6
x
+
6
y
+
3
z
=
8
\displaystyle {6}{x}+{6}{y}+{3}{z}={8}
6
x
+
6
y
+
3
z
=
8
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