According to ques,
points are:
![\[\left( 2,\text{ }1,\text{ }0 \right),\text{ }\left( 3,\text{ }2,\text{ }2 \right)\text{ }and\text{ }\left( 3,\text{ }1,\text{ }7 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5ea57a324f56e9b8167070c48680ff7d_l3.png "Rendered by QuickLaTeX.com")
Since,
equation of the plane passing through the points
![\[\left( {{x}_{1}},\text{ }{{y}_{1}},\text{ }{{z}_{1}} \right),\text{ }\left( {{x}_{2}},\text{ }{{y}_{2}},\text{ }{{z}_{2}} \right)\text{ }and\text{ }\left( {{x}_{3}},\text{ }{{y}_{3}},\text{ }{{z}_{3}} \right)\text{ }is:\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3ca675cdfcef0eb86542e731d95fbe66_l3.png "Rendered by QuickLaTeX.com")
![\[\left( x\text{ }\text{ }2 \right)\text{ }\left( -21 \right)\text{ }\text{ }\left( y\text{ }\text{ }1 \right)\left( 7\text{ }+\text{ }2 \right)\text{ }+\text{ }z\text{ }\left( 3 \right)\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-482fbdead54786980771416ad02dd612_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[-21\text{ }\left( x\text{ }\text{ }2 \right)\text{ }\text{ }9\left( y\text{ }\text{ }1 \right)\text{ }+\text{ }3z\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-27c2e41bca286f0ef2a72582ad73a29b_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[-21x\text{ }+\text{ }42\text{ }\text{ }9y\text{ }+\text{ }9\text{ }+\text{ }3z\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6c4f28086a8e1641c08fcfc9e0fce6af_l3.png "Rendered by QuickLaTeX.com")
Or,
![\[-21x\text{ }\text{ }9y\text{ }+\text{ }3z\text{ }+\text{ }51\text{ }=\text{ }0\Rightarrow 7x\text{ }+\text{ }3y\text{ }\text{ }z\text{ }\text{ }17\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-f24296712dfd286611732bd205daabeb_l3.png "Rendered by QuickLaTeX.com")
Hence,
Required equation of plane is:
![\[7x\text{ }+\text{ }3y\text{ }\text{ }z\text{ }\text{ }17\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1ef09763f68359eb6893af60ccaf7fc7_l3.png "Rendered by QuickLaTeX.com")
According to ques,
points are:
Since,
equation of the plane passing through the points
Or,
Or,
Or,
Hence,
Required equation of plane is: