Question

The straight lines $L_1\equiv 4x-3y+2=0,L_2\equiv 3x+4y-4=0$ and $L_3\equiv x-7y+6=0$

• A. form a right-angled triangle
• B. form a right-angled isosceles triangle
• C. are concurrent
• D. none of these

Answer 1

The correct option is C are concurrent

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

then lines are concurrent.

Now ,$\left|\begin{array}{ccc}4& -3& 2\\ 3& 4& -4\\ 1& -7& 6\end{array}\right|=4(24-28)+3(18+4)+2(-21-4)=-16+66-50=0$
Hence, lines are concurrent.