According to ques,
\[~O\text{ }\left( 0,\text{ }0,\text{ }0 \right)\text{ }and\text{ }A\left( a,\text{ }b,\text{ }c \right)\]
Hence,
the direction ratios of OA :
\[a\text{ }\text{ }0,\text{ }b\text{ }\text{ }0,\text{ }c\text{ }\text{ }0\text{ }=\text{ }a,\text{ }b,\text{ }c\]
also, the direction ratios of the normal to the plane are \[\left( a,\text{ }b,\text{ }c \right).\]
Since, the equation of the plan passing through the point A(a, b, c) is:
\[a\left( x\text{ }\text{ }a \right)\text{ }+\text{ }b\left( y\text{ }\text{ }b \right)\text{ }+\text{ }c\left( z\text{ }\text{ }c \right)\text{ }=\text{ }0\]
Or,
\[ax\text{ }\text{ }{{a}^{2}}~+\text{ }by\text{ }\text{ }{{b}^{2}}~+\text{ }cz\text{ }\text{ }{{c}^{2}}~=\text{ }0\]
Or,
\[ax\text{ }+\text{ }by\text{ }+\text{ }cz\text{ }=\text{ }{{a}^{2}}~+\text{ }{{b}^{2}}~+\text{ }{{c}^{2}}\]
Hence,
Required equation of the plane is:
\[ax\text{ }+\text{ }by\text{ }+\text{ }cz\text{ }=\text{ }{{a}^{2}}~+\text{ }{{b}^{2}}~+\text{ }{{c}^{2}}\]