| Statement 1: If \[({{a}_{1}}x+{{b}_{1}}y+{{c}_{1}})+({{a}_{2}}x+{{b}_{2}}y+{{c}_{2}})\]\[+\,({{a}_{3}}x+{{b}_{3}}y+{{c}_{3}})=0\]then lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0,\]\[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\]and \[{{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}=0\]cannot be parallel. |
| Statement 2: If sum of three straight lines equations is identically zero then they are either concurrent or parallel. |
A) Statement 1 is true, statement 2 is true and statement 2 is correct explanation for statement 1.
B) Statement 1 is true, statement 2 is true and statement 2 is NOT the correct explanation for statement.
C) Statement 1 is true, statement 2 is false.
D) Statement 1 is false, statement 2 is true.
Correct Answer: D
Solution :
The statement 1 is false since \[(x-2)+(2x-3)+(5-3x)=0\] but the lines \[x-2=0,\]\[2x-3=0\]and \[5-3x=0\]are parallel. The Statement 2 is a standard true result whose more general from is: if \[{{L}_{1}}=0\], \[{{L}_{2}}=0\],\[{{L}_{3}}=0\]be three lines. If we could find \[\lambda ,\mu ,\,v\](not all zero) such that \[{{L}_{1}}=0,\,\,{{L}_{2}}=0,\,{{L}_{3}}=0\]are either concurrent or are parallel.
You need to login to perform this action.
You will be redirected in
3 sec
