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)|` is equal to

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 A(x_(1),y_(1)),B(x_(2),y_(2))andC(x_(3),y_(3)) are vertices of on equilateral triangle with each side equal to a units, than prove that |(x_(1),y_(1),2),(x_(2),y_(2),2),(x_(3),y_(3),2)|^(2)=3a^(4)

If A(x_1, y_1),B(x_2, y_2)a n dC(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 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 unit , then prove that, |{:(x_1,y_1,2),(x_2,y_2,2), (x_3,y_3,2):}|^2=3a^4

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=3 a^4

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 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 A(x_(1),y_(1)),B(x_(2),y_(2)) and C(x_(3),y_(3)) are the vertices of a triangle then excentre with respect to B is