An equilateral triangle has each side equal to a, If `(x_1, y_1) , (x_2, y_2) , (x_3, y_3)` are the vertices of the triangle then `|[x_1 , y_1, 1] , [x_2, y_2, 1] , [x_3, y_3, 1]|^2=`

An equilateral triangle has each side equal to a,If (x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3)) are the vertices of the triangle then det[[x_(1),y_(1),1x_(2),y_(2),1x_(3),y_(3),1]]^(2)=

If A(x_1,y_1),B(x_2,y_2),C(x_3,y_3) are the vertices of the triangle then find area of triangle

If A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3)) are the vertices of the triangle then show that:'

An equilateral triangle has each of its sides of length 6 cm. If (x_1, y_1);(x_2, y_2)&(x_3, y_3) are its vertices, then the value of the determinant |x_1y_1 1x_2y_2 1x_3y_3 1|^2 is equal to: 192 (b) 243 (c) 486 (d) 972

An equilateral triangle has each of its sides of length 6 cm. If (x_1, y_1);(x_2, y_2)&(x_3, y_3) are its vertices, then the value of the determinant |x_1y_1 1x_2y_2 1x_3y_3 1|^2 is equal to: 192 (b) 243 (c) 486 (d) 972

An equilateral triangle has each of its sides of length 6 cm. If (x_1, y_1);(x_2, y_2)&(x_3, y_3) are its vertices, then the value of the determinant |x_1y_1 1x_2y_2 1x_3y_3 1|^2 is equal to: 192 (b) 243 (c) 486 (d) 972

An equilateral triangle has each of its sides of length 6 cm. If (x_1, y_1);(x_2, y_2)&(x_3, y_3) are its vertices, then the value of the determinant |x_1y_1 1x_2y_2 1x_3y_3 1|^2 is equal to: 192 (b) 243 (c) 486 (d) 972

An equilateral triangle has each of its sides of length 6c mdot If (x_1, y_1);(x_2, y_2)&(x_3, y_3) are its vertices, has the value of the determinant |x_1y_1 1x_2y_2 1x_3y_3 1| is equal to: 192 b. 243 c. 486 d. 972

If (x_1,y_1) , (x_2,y_2) and (x_3,y_3) are the vertices of a triangle whose area is k square units, then |{:(x_1,y_1,4),(x_2,y_2,4),(x_3,y_3,4):}|^2 is

If the co-ordinates of the vertices of an equilateral trianlg with sides of length 'a' are (x_1,y_1),(x_2,y_2),(x_3,y_3) , then Prove that |{:(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1):}|^2=(3/4)a^4.