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STATEMENT-1: The lines a(1)x+b(1)y+c(1)=...

STATEMENT-1: The lines `a_(1)x+b_(1)y+c_(1)=0a_(2)x+b_(2)y+c_(2)=0,a_(3)x+b_(3)y+c_(2)=0` are concurrent if `|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=0.`
STATEMENT-2: The area of the triangle formed by three concurrent lines is always zero.

A

Statement -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 4

B

Statement-1 is True , Statement-2 is True , Statement -2 is not a correct explanation for Statement - 1 .

C

Statement-1 is True , Statement - 2 is False .

D

Statement - 1 is False , Statement -2 is True .

Text Solution

Verified by Experts

The correct Answer is:
A
The area of triangle formed by the lines `a_(1)x + b_(1) y + c_(1) = 0 , a_(2) x + b_(2)y + c_(2) = 0` and `a_(3) x + b_(3) y + c_(3) = 0` is
`Delta = (1)/(2C_(1) C_(2)C_(3)) |{:(a_(1), b_(1), c_(1)), (a_(2) ,b_(2), c_(2)) , (a_(3), b_(3), c_(3)):}|^(2)`
where `C_(1) , C_(2) , C_(3)` are cofactors of `c_(1) , c_(2) , c_(3)` respectively in the matrix
`[{:(a_(1), b_(1), c_(1)), (a_(2) ,b_(2), c_(2)) , (a_(3), b_(3), c_(3)):}]`
If the lines are concurrent , then `Delta = 0 implies |{:(a_(1), b_(1), c_(1)), (a_(2) ,b_(2), c_(2)) , (a_(3), b_(3), c_(3)):}|` = 0
So , statement -2 is true . Also , statement - 1 is true and statement - 2 is a correct explanation for statement -1 .
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