According to ques,
points are: \[\left( 2,\text{ }1,\text{ }0 \right),\text{ }\left( 3,\text{ }2,\text{ }2 \right)\text{ }and\text{ }\left( 3,\text{ }1,\text{ }7 \right)\]
Since,
equation of the plane passing through the points
\[\left( {{x}_{1}},\text{ }{{y}_{1}},\text{ }{{z}_{1}} \right),\text{ }\left( {{x}_{2}},\text{ }{{y}_{2}},\text{ }{{z}_{2}} \right)\text{ }and\text{ }\left( {{x}_{3}},\text{ }{{y}_{3}},\text{ }{{z}_{3}} \right)\text{ }is:\]
\[\left( x\text{ }\text{ }2 \right)\text{ }\left( -21 \right)\text{ }\text{ }\left( y\text{ }\text{ }1 \right)\left( 7\text{ }+\text{ }2 \right)\text{ }+\text{ }z\text{ }\left( 3 \right)\text{ }=\text{ }0\]
Or,
\[-21\text{ }\left( x\text{ }\text{ }2 \right)\text{ }\text{ }9\left( y\text{ }\text{ }1 \right)\text{ }+\text{ }3z\text{ }=\text{ }0\]
Or,
\[-21x\text{ }+\text{ }42\text{ }\text{ }9y\text{ }+\text{ }9\text{ }+\text{ }3z\text{ }=\text{ }0\]
Or,
\[-21x\text{ }\text{ }9y\text{ }+\text{ }3z\text{ }+\text{ }51\text{ }=\text{ }0\Rightarrow 7x\text{ }+\text{ }3y\text{ }\text{ }z\text{ }\text{ }17\text{ }=\text{ }0\]
Hence,
Required equation of plane is:
\[7x\text{ }+\text{ }3y\text{ }\text{ }z\text{ }\text{ }17\text{ }=\text{ }0\]