Find the coordinates of the centroid fof 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 |(2a,x_(1),y_(1)),(2b,x_(2),y_(2)),(2c,x_(3),y_(3))| = (abc)/2 != 0 , then the area of the triangle whose vertices are ((x_(1))/a,(y_(1))/a),((x_(2))/b,(y_(2))/b)and ((x_(3))/c,(y_(3))/c)

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 z_(1),z_(2),z_(3) are the vertices of an equilateral triangle in the Argand plane, then (z_(1)^(2)+z_(2)^(2)+z_(3)^(3))=lambda(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)) holds true when :

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

Complex numbers z_(1),z_(2),z_(3) are the vertices of A,B,C respectively of an equilteral triangle. Show that z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).

Let a(4, 2), B(6, 5) and C(1, 4) be the vertices of Delta ABC . If A (x_(1), y_(1)), B(x_(2), y_(2)) and C(x_(3), y_(3)) are the vertices of Delta ABC , find the coordinates of the centroid of the triangle.

Find the angle between the pair of lines (x+3)/(3)=(y-1)/(5)=(z+3)/(4) and (x+1)/(1)=(y-4)/(1)=(z-5)/(2)