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L1 = x + 3y-5=0, L2= 3x-ky-1=0 , L3 = 5x...

`L_1 = x + 3y-5=0, L_2= 3x-ky-1=0 , L_3 = 5x + 2y-12 = 0 ` are concurrent if k=

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`(A)` Solving equations `L_(1)` and `L_(3)` ,
`(x)/(-36+10)=(y)/(-25+12)=(1)/(2-15)`
`:.x=2`, `y=1`
`L_(1)`, `L_(2)`, `L_(3)` are concurrent, if point `(2,1)` lies on `L_(2)`
`:. 6-k-1=0impliesk=5`
`(B)` Either `L_(1)` is parallel to `L_(2)` or `L_(3)` is parallel to `L_(2)`, then
`(1)/(3)=(3)/(-k)` or `(3)/(5)=(-k)/(2)impliesk=-9`
or `k=(-6)/(5)`
`(C )` `L_(1)`, `L_(2)`, `L_(3)` form a triangle, if they are not concurrent, or not parallel.
`:.k ne 5`, `-9`, `-(6)/(5)impliesk=(5)/(6)`
`(D)` `L_(1)`, `L_(2)`, `L_(3)` do not form a triangle, if
`k=5`, `-9`, `-(6)/(5)`
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