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Consider the lines given by L(1):x+3y-...

Consider the lines given by
`L_(1):x+3y-5=0`
`L_(2):3x-ky-1=0`
`L_(3):5x+2y-12=0`
Match the following lists.

Text Solution

Verified by Experts

The correct Answer is:
`a to s;" b" to p,q; " c" to r; " d" to p,q,s`
Given lines are
`L_(1): x+3y-5 = 0`
`L_(2): 3x-ky-1 = 0`
`L_(3): 5x+2y-12 = 0`
`L_(1) " and " L_(3)` intersect at (2, 1)
`therefore L_(1), L_(2), L_(3)` are concurrent if
6-k-1 = 0 or k=5
`"For " L_(1), L_(2)` to be parallel
`(1)/(3) = (3)/(-k) rArr k = -9`
`"For " L_(2), L_(3)` to be parallel
`(3)/(5) = (-k)/(2) rArr k = (-6)/(5)`
Thus, for k = 5, lines are concurrent and for `k = -9, (-6)/(5),` at least two lines are parallelk. So, for these values of k, lines will not form triangle.
Obviously, for `k ne 5, -9, (-6)/(5),` lines form triangle.
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