Question

Three lines given by $L_1:a_{1}x+b_{1}y+c_1=0,L_2:a_{2}x+b_{2}y+c_2=0\text{and}{L}_3:a_{3}x+b_{3}y+c_3=0$ are always concurrent given that

$\left|\begin{array}{cccc}{a}_1& b_1& c_1& \\ a_2& b_2& c_2& \\ a_3& b_3& c_3& \end{array}\right|=0$

• A. False
• B. True

Answer 1

The correct option is A

False

You have already seen that the condition required for concurrency of three lines can be given in determinant form as given in the previous part. But this cannot be applied everywhere blindly. The condition given by the determinant is a necessary condition but not sufficient. If the determinant is zero it can either mean that they are concurrent or they are parallel to each other. So we need to make sure first that the lines given are not parallel before we apply the actual condition.

So a necessary test for parallel lines has to be done by checking the coefficients of the lines.