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 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

Find the value of x, If [[3x+y,-y],[2y-x,3]]=[[1,2],[-5,3]]

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 A(x_1, y_1),B(x_2, y_2) and C(x_3,y_3) are vertices of an equilateral triangle whose each side is equal to a , then prove that |[x_1,y_1, 2],[x_2,y_2, 2],[x_3,y_3, 2]|^2=3a^4

If the points (x_1,y_1),(x_2,y_2)and(x_3,y_3) are collinear, then the rank of the matrix {:[(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)]:} will always be less than

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

If a x_1^2+b y_1^2+c z_1^2=a x_2 ^2+b y_2 ^2+c z_2 ^2=a x_3 ^2+b y_3 ^2+c z_3 ^2=d ,a x_2 x_3+b y_2y_3+c z_2z_3=a x_3x_1+b y_3y_1+c z_3z_1=a x_1x_2+b y_1y_2+c z_1z_2=f, then prove that |(x_1, y_1, z_1), (x_2, y_2, z_2), (x_3,y_3,z_3)|=(d-f){((d+2f))/(a b c)}^(1//2)

If (x_i,y_i),i=1,2,3 are the vertices of an equilateral triangle such that (x_1+2)^2+(y_1-3)^2=(x_2+2)^2+(y_2-3)^2=(x_3+2)^2+(y_3-3)^2 , then find the value of (x_1+x_2+x_3)/(y_1+y_2+y_3)

If [x+y x-y]=[2 1 4 3][1-2] , then write the value of (x ,\ y) .

If (x_i ,y_i),i=1,2,3, are the vertices of an equilateral triangle such that (x_1+2)^2+(y_1-3)^2=(x_2+2)^2+(y_2-3)^2=(x_3+2)^2+(y_3-3)^2, then find the value of (x_1+x_2+x_3)/(y_1+y_2+y_3) .