I tried searching the below on MSE site but didn't find any useful answer to the below question .
Prove that the line of intersection of the planes $a_1+b_1+c_1+d_1=0, a_2+b_2+c_2+d_2=0 $ is coplanar with the line of intersection of the planes $a_3+b_3+c_3+d_3=0 \;,\;a_4+b_4+c_4+d_4=0 $ iff $$det\left[\begin{array}{rrrr} a_1&b_1&c_1&d_1\\ a_2&b_2&c_2&d_2\\ a_3&b_3&c_3&d_3\\ a_4&b_4&c_4&d_4 \end{array}\right]=0$$