If the co-ordinates of the vertices of an equilateral triangle with sides of length `a` are `(x_1,y_1), (x_2, y_2), (x_3, y_3),` then `|[x_1,y_1,1],[x_2,y_2,1],[x_3,y_3,1]|=(3a^4)/4`

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.

If the coordinates of the vertices of an equilateral triangle with sides of length a are (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) then |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2=(3a^(4))/4

If the coordinates of the vertices of an equilateral triangle with sides of length a are (x_(1),y_(1)),(x_(2),y_(2)) and (x_(3),y_(3)) then |(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|^2=(3a^(4))/4

Find the coordinates of the centroid of the triangle whose vertices are (x_1,y_1,z_1) , (x_2,y_2,z_2) and (x_3,y_3,z_3) .

If the vertices of an equilateral triangle are A(x_1,y_1), B(x_2,y_2) and C(x_3,y_3) then show that |(x_1, y_1,2),(x_2, y_2, 2),(x_3,y_3,2)|^2 = 3a^4 , 'a' being the length of each side of the triangle.

Find the co-ordinates of the centroid of the triangle whose vertices are (x_(1),y_(1),z_(1)), (x_(2),y_(1),z_(2)) and (x_(3),y_(3),z_(3)) .

What are the coordinates of the centroid of the triangle with vertices (x_1,y_1) (x_2,y_2) and (x_3,y_3)

Write the formula for the area of the triangle having its vertices at (x_1,\ y_1),\ \ (x_2,\ y_2) and (x_3,\ y_3) .