Question

Statement-1 : If three lines $L_1:a_{1}x+b_{1}y+c_1=0,L_2:a_{2}x+b_{2}y+c_2=0$ and $L_3:a_{3}x+b_{3}y+c_3=0$ are concurrent
lines, then $\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_2& b_3\end{array}\right|=0.$
Statement-2 : If $\left|\begin{array}{ccc}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_2& b_3\end{array}\right|=0$ then the lines $L_1,L_2,L_3$ must be concurrent.

• A. Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for Statement-1.
• B. Statement -1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
• C. Statement -1 is false, Statement-2 is true.
• D. Statement -1 is true, Statement-2 is false.

Answer 1

Answer: (D)

If $\Delta =0$ then two of rows or column are proportional which is possible even if three lines are parallel or two of them are coincident.