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Question

If the lines a1x+b1y+1=0,a2x+b2y+1=0and a3x+b3y+1=0 are concurrent, then the points (a1,b1),(a2,b2) and (a3,b3) will be collinear.

A
True
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B
False
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Solution

The correct option is A True
If the lines a1x+b1y+1=0,a2x+b2y+1=0and a3x+b3y+1=0 are concurrentThen, a1b11a2b21a3b31∣ ∣ = 0This is the required condition for the concurrenceof three straight lines. Also we can say that thetriangle formed using the points (a1, b1), (a2, b2), and (a3, b3) is zero area. Thus, the points arecollinear.

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