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Question

Question: If a<sub>1</sub>x + b<sub>1</sub>x + c<sub>1</sub> = 0, a<sub>2</sub>x + b<sub>2</sub>y + c<sub>2</s...

If a1x + b1x + c1 = 0, a2x + b2y + c2 = 0 and

a3x + b3y + c3 = 0 are three lines and D = a1 b1c1a2 b2c2a3 b3c3\left| \begin{array} { l l l } \mathrm { a } _ { 1 } & \mathrm {~b} _ { 1 } & \mathrm { c } _ { 1 } \\ \mathrm { a } _ { 2 } & \mathrm {~b} _ { 2 } & \mathrm { c } _ { 2 } \\ \mathrm { a } _ { 3 } & \mathrm {~b} _ { 3 } & \mathrm { c } _ { 3 } \end{array} \right| then the lines will form a triangle if

A

D = 0,a1b2 – a2b1 = 0

B

D = 0, a2b3 – a3b2¹ 0

C

D ¹ 0

D

None of these

Answer

D ¹ 0

Explanation

Solution

If these lines form a triangle then point of intersection of any two lines must not lie on third line, D ¹ 0