Mathematics - Straight Lines Question with Solution | TestHub

Statement I: If $\left|a_1{b}_1{c}_1{a}_2{b}_2{c}_2{a}_3{b}_3{c}_3\right|=0,\frac{a_1}{b_1}\ne \frac{a_2}{b_2}\ne \frac{a_3}{b_3}$ then the lines $a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0$ and $a_{3}x+b_{3}y+c_3=0$ are concurrent.

Statement II: Area of the triangle formed by $a_{1}x+b_{1}y+c_1=0,a_{2}x+b_{2}y+c_2=0$ and $a_{3}x+b_{3}y+c_3=0$ is $\frac{1}{2}\Vert a_1{b}_1{c}_1{a}_2{b}_2{c}_2{a}_3{b}_3{c}_3\Vert$.