Consider the planes P1:2x+y+z+4=0,P2:y−z+4=0 and P3:3x+2y+z+8=0. Let L1L2,L3 be the lines of intersection of the planes P2 and P3,P3 and P1, and P1 and P2respectively.then

Observe that the lines L1,L2&L3 are parallel  to the vector i^−j^−k^ Also, Δ=0=Δ1&b1c2≠b1c1 Hence the three planes intersect in a line. P1=2x+y+z+4=0P2=0x+y−z+4=0P3=3x+2y+z+8=0P2 and P3 gives line L1  Vector parallel to line L1i^j^k^01−1321=3i^−3j^−3k^=3[i^−j^−k^]Similarly  Vector parallel to L2,P3 and P1=i^    j^    k^2    1    13    2    1 =−2i^+2j^+k^=−2(i^−j^−k^) =−i^+j^+k^=−i^−j^−k^Similarly  Vector parallel to L3,P1 and P2=i^j^k^21101−1=−2i^−−2j^+2k^We can see all the lines are parallel to vector(i^−j^−k^) Also 2x+y+z=−40x+y−z=−43x+2y+z=−8Δ=21101−1321⇒2(1+2)−1(0+3)+1(0−3)Δ2=2−410−4−13−81=0=−421101−1321=0Δ3=0So all planes intersection in line L.