Solution:
Comparing each of them with r.(ai^+bj^)+c=0
we get,
a1=4,b1=3,c1=−1a2=−2,b2=1,c2=−1a3=1,b3=2,c3=−1
For these lines to be concurrent, they must satisfy following:
∣∣a1a2a3b1b2b3c1c2c3∣∣=0
Take LHS
=∣∣a1a2a3b1b2b3c1c2c3∣∣
Putting above values
=∣∣4−21312−1−1−1∣∣
=4∣∣12−1−1∣∣−3∣∣−21−1−1∣∣+(−1)∣∣−2112∣∣
=4(−1+2)−3(2+1)−1(−4−1)=4−9+5=9−9=0
= RHS
Thus, above lines are concurrent.
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