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_1y_1 1x_2y_2 1x_3y_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 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 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)(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)=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)

If (x-1)^2+(y-2)^2 = (x-1)(y-2) , where x and y are integers, then the value of 2x + 3y is

If 2^(x+y) = 6^(y) and 3^(x-1) = 2^(y+1) , then the value of (log 3 - log 2)//(x-y) is