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Question

Consider the lines given by
L1:x+3y5=0, L2:3xky1=0, L3:5x+2y12=0

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Solution

(a) L1 and L3 intersect at (1,2) and it will lie on L2 if k=5
(b) Condition of parallelism gives
31=k3=15 k=9

(b)(p)
Also 33=k2=112 k=65 (b)(q)

(b)(p,q)
(c) If k5,9,65 i.e. (a) and (b) are ruled out and hence they form a triangle.

(c)(r)
(d) Exclude the cases of (a) and (b) i.e.,

k=5,9,65, they will not form a triangle.

(d)(p,q,s)

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