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If (x(1)-x(2))^(2) + (y(1)-y(2))^(2) =a^...

If `(x_(1)-x_(2))^(2) + (y_(1)-y_(2))^(2) =a^(2), (x_(2)-x_(3))^(2) + (y_(2)-y_(3))^(2) = b^(2), (x_(3)-x_(1))^(2) (y_(3)-y_(1))^(2) =c^(2)` and `|{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|^(2) = (a+b+c)(b+c-a)(c+a-b)(a+b-c)` then the value of `lambda` is:

Text Solution

Verified by Experts

The correct Answer is:
`4.00`
`lambda|{:(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1):}|=(a+b+c)(b+c-a)(c+a-b)(a+b-c)`
`rArr 4lambda Delta^(2) = 16 s(s-a) (s-b)(s-c)`
`rArr 4lambda Delta^(2) = 16 Delta^(2)`
`rArr 4lambda = 16 rArr lambda =4`
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