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Q.

Consider the lines:
L1:2x−y+5=0 ,
L2:x+ky−1=0 ,
L3:kx+2y+4=0 .
If the lines  L1,L2 and L3 do not form a triangle, then absolute value of sum of all possible  values of  k is

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answer is 2.7.

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Detailed Solution

Triangle will not be formed if
 L1||L2⇒2=−1k⇒k=−12
or  L1||L3⇒2=−k2⇒k=−4
or L2||L3⇒−1k=−k2⇒k2=2⇒k=±2
or  L1,L2,L3 are concurrent
 ⇒k=−65,3
sum =−12−4−65+3=−2.7

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