If `|(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|=|(a_(1),b_(1),1),(a_(2),b_(2),1),(a_(3),b_(3),1)|`, then the two triangles with vertices `(x_(1),y_(1)),(x_(2),y_(2)),(x_(3),y_(3))` and `(a_(1),b_(1)),(a_(2),b_(2)),(a_(3),b_(3))` must be

If the lines a_(1)x+b_(1)y=1,a_(2)x+b_(2)y=1,a_(3)x+b_(3)y=1, are concurrent then the points (a_(1),b_(1)),(a_(2),b_(2)),(a_(3),b_(3))

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 |(1+a_(1),a_(2),a_(3)),(a_(1),1+a_(2),a_(3)),(a_(1),a_(2),1+a_(3))|=0 then a_(1)+a_(2)+a_(3)=

If Delta_(1)=|{:(a_(1)^(2)+b_(1)+c_(1),a_(1)a_(2)|b_(2)|c_(2),a_(1)a_(3)+b_(3)+c_(3)),(b_(1)b_(2)+c_(1),b_(2)^(2)+c_(2),b_(2)b_(3)+c_(3)),(c_(1)c_(3),c_(2)c_(3),c_(3)^(2)):}|" and " Delta_(2)=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}| , then find the value of (Delta_(1))/(Delta_(2)) .

A(3x_(1), 3y_(1)), B(3x_(2), 3y_(2)), C(3x_(3), 3y_(3)) are vertices of a triangle with orthocentre H at (x_(1)+ x_(2)+ x_(3), y_(1)+y_(2)+y_(3)) , then the angleABC=

If (a_(1), b_(1), c_(1)), (a_(2), b_(2), c_(2)) are d.r.'s of two perpendicular lines then

If (x_(1), y_(1)), (x_(2), y_(2)), (x_(3), y_(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 x_(1)+x_(2)+x_(3)+2(y_(1)+y_(2)+y_(3))=