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Question -

Show that the straight lines L1 = (b + c)x + ay + 1 = 0,L2 = (c + a)x + by + 1 = 0 and L3 = (a + b)x +cy + 1 = 0 are concurrent.



Answer -

Given:

L1 =(b + c)x + ay + 1 = 0

L2 =(c + a)x + by + 1 = 0

L3 =(a + b)x + cy + 1 = 0

The given lines can bewritten as follows:

(b + c) x + ay + 1 = 0… (1)

(c + a) x + by + 1 = 0… (2)

(a + b) x + cy + 1 = 0… (3)

Consider the followingdeterminant.

Hence proved, thegiven lines are concurrent.

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