This a problem taken in one of the standard text book in calculus. This is is not a homework. Can I ask some tips on how to proceed? I tried looking on the net but cant find a good one.
Problem. Find a condition that the three planes \begin{align} a_1x+b_1y+c_1z+d_1=0\\ a_2x+b_1y+c_2z+d_2=0\\ a_3x+b_1y+c_3z+d_3=0 \end{align} either have a line in common or have a point in common.
Consider the condition as a system of linear equations. If $Det A\neq 0$ in non-homogeneous case, the system has unique solution, that is the planes has a common point, if not it can be have $2$ or $1$ independent equation, if there is $2$ independent equation they have a common line, by Gaussian elimination method you can find the number of independent equations. in the case $1$ independent equation the plans are the same.