Answer
$5x-3y-z=35$
Work Step by Step
Equation of the plane in component form is
$\begin{vmatrix}x-x_{1}&y-y_{1}&z-z_{1}\\x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\x_{3}-x_{1}&y_{3}-y_{1}&z_{3}-z_{1}\end{vmatrix}=0$
$\implies \begin{vmatrix}x-6&y+2&z-1\\5-6&-3+2&-1-1\\7-6&0+2&0-1\end{vmatrix}=0$
$\implies \begin{vmatrix}x-6&y+2&z-1\\-1&-1&-2\\1&2&-1\end{vmatrix}=0$
Expanding along first row, we have
$(x-6)(1+4)-(y+2)(1+2)+(z-1)(-2+1)=0$
$\implies 5x-30-3y-6-z+1= 0$
or $5x-3y-z= 35$
