A) \[{{L}_{1}}||{{L}_{4}},{{L}_{2}}||{{L}_{3}},{{L}_{1}}\]intersect \[{{L}_{4}}.\]
B) \[{{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{1}}\] intersect \[{{L}_{2}}.\]
C) \[{{L}_{1}}\bot {{L}_{2}},{{L}_{2}}||{{L}_{3}},{{L}_{1}}\] intersect \[{{L}_{4}}.\]
D) \[{{L}_{1}}\bot {{L}_{2}},{{L}_{1}}||{{L}_{3}},{{L}_{2}}\] intersect \[{{L}_{4}}.\]
Correct Answer: D
Solution :
Consider the lines \[{{L}_{1}}:x-y=1\] \[{{L}_{2}}:x+y=1\] \[{{L}_{3}}:2x+2y=5\] \[{{L}_{4}}:2x-2y=7\] \[{{L}_{1}}\bot {{L}_{2}}\] is correct statement (\[\because \]Product of their slopes = - 1) \[{{L}_{1}}\bot {{L}_{3}}\] is also correct statement (\[\because \]Product of their slopes = - 1) Now, \[{{L}_{2}}:x+y=1\] \[{{L}_{4}}:2x-2y=7\] \[\Rightarrow \]\[2x-2(1-x)=7\]\[\Rightarrow \]\[2x-2+2x=7\] \[\Rightarrow \]\[x=\frac{9}{4}\]and\[y=\frac{-5}{4}\] Hence, \[{{L}_{2}}\]intersects\[{{L}_{4}}.\]
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