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 `k|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|=(a+b+c)(b+c-b)(c+a-b)xx(a+b-c)` , then the value of `k` is `1` b. `2` c. `4` d. none of these

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 and (x_3-x_1)^2+(y_3-y_1)^2=c^2 then prove that 4|{:(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)

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 2s=a+b+c then what willl be the value of 1/4|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|^2

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 2s=a+b+c then what willl be the value of 1/4|[x_1,y_1, 1],[x_2,y_2, 1],[x_3,y_3, 1]|^2

If (x_1-x_2)^2+(y_1-y_2)^2=144 ,(x_2-x_3)^2+(y_2-y_3)^2=25 and (x_3-x_1)^2+(y_3-y_1)^2=169 , then the value of |[x_1,y_1, 1],[x_2,y_2 ,1],[x_3,y_3, 1]|^2 is 30 (b) 30^2 (c) 60 (d) 60^2

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 k[|(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 k a)1 b)2 c)4 d)none of these

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 2s=a+b+c then (1)/(4)det[[x_(2),y_(2),1x_(3),y_(3),1]]^(2)

If (x_(1)-x_(2))^(2)+(y_(1)-y_(2))^(2)=144,(x_(2)-x_(3))^(2)+(y_(2)-y_(3))^(2)=25 and (x_(3)-x_(1))^(2)+(y_(3)-y_(1))^(2)=169, then the value of det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2) is 30(b)30^(2)(c)60(d)60^(2)

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). where a,b,c are positive then prove that 4 |{:(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)