Answer
The equation of the plane is
$$4y-9x-3z=0.$$
Work Step by Step
The equation of the plane is given by
$$
\left|\begin{array}{rrr}{x} & {y} & {z}&{1} \\ {0} & {0} & {0}&{1}\\ {1} & {0} & {3}&{1} \\{0}&{3}&{4}&{1}\end{array}\right|= 0.
$$
So, we have
$$
\left|\begin{array}{rrr}{x} & {y} & {z}&{1} \\ {0} & {0} & {0}&{1}\\ {1} & {0} & {3}&{1} \\{0}&{3}&{4}&{1}\end{array}\right|= \left|\begin{array}{rrr}{x} & {y} & {z} \\ {1} & {0} & {3} \\{0}&{3}&{4} \end{array}\right|=-(4y-3z)-3(3x)=-4y+9x+3z=0.
$$
Hence, the equation of the plane is
$$4y-9x-3z=0.$$
