Condition for concurrent lines (Three lines aix+biy+ci=0 meet at one point iff this 3×3 determinant is)

jee-mainjee-advanced

Three lines aix+biy+ci=0 meet at one point iff this 3×3 determinant is zero.

What each symbol means

SymbolWhat it stands for
ai,bi,ciCoefficients of the i-th line

When to use this

Lines not necessarily pairwise non-parallel; determinant zero is concurrency test.