According to ques,

Point is \[\left( 3,\text{ }0,\text{ }1 \right)\] and the equation of planes are:

\[x\text{ }+\text{ }2y\text{ }=\text{ }0\text{ }\ldots .\text{ }\left( i \right)\]

and

\[3y\text{ }\text{ }z\text{ }=\text{ }0\text{ }\ldots .\text{ }\left( ii \right)\]

Equation of any line l passing through (3, 0, 1) is:

\[~\left( x\text{ }\text{ }3 \right)/a\text{ }=\text{ }\left( y\text{ }\text{ }0 \right)/b\text{ }=\text{ }\left( z\text{ }\text{ }1 \right)/c\]

the direction ratios of the normal to plane (i) and plane (ii) are:

\[~\left( 1,\text{ }2,\text{ }0 \right)\text{ }and\text{ }\left( 0,\text{ }3,\text{ }1 \right).\]

As the line is parallel to both the planes,

\[1.a\text{ }+\text{ }2.b\text{ }+\text{ }0.c\text{ }=\text{ }0\Rightarrow a\text{ }+\text{ }2b\text{ }+\text{ }0c\text{ }=\text{ }0\]

and

\[0.a\text{ }+\text{ }3.b\text{ }\text{ }1.c\text{ }=\text{ }0\Rightarrow 0a\text{ }+\text{ }3b\text{ }\text{ }c\text{ }=\text{ }0\]