`Delta=|[a_(1),b_(1)],[a_(2),b_(2)]|` and `A_(1),B_(1),A_(2),B_(2)` are cofactor of `a_(1),b_(1),a_(2),b_(2)` respectively then ,`|[A_(1),B_(1)],[A_(2),B_(2)]|` has value equal to

if Delta=det[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

if quad /_=[[a_(1),b_(1),c_(1)a_(2),b_(2),c_(2)a_(3),b_(3),c_(3)]]

If the points (a_(1),b_(1))m(a_(2),b_(2))" and " (a_(1)-a_(2),b_(2)-b_(2)) are collinear, then prove that a_(1)/a_(2)=b_(1)/b_(2)

Show that |[a_(1),b_(1),-c_(1)],[-a_(2),-b_(2),c_(2)],[a_(3),b_(3),-c_(3)]|=|[a_(1),b_(1),c_(1)],[a_(2),b_(2),c_(2)],[a_(3),b_(3),c_(3)]|

If, in D={:[(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))]:}, the co-factor of a_(r)" is "A_(r), then , c_(1)A_(1)+c_(2)A_(2)+c_(3)A_(3)=

If G_(1),G_(2) are centroids of triangles A_(1),B_(1),C_(1) and A_(2),B_(2),C_(2) respectively, then bar(A_(1)A_(2))+bar(B_(1)B_(2))+bar(C_(1)C_(2)) =

if a,A_(1),A_(2),A_(3)......,A_(2n),b are in A.P.then sum_(i=1)^(2n)A_(i)=(a+b)

If (a_(1)//x)+(b_(1)//y)=c_(1),(a_(2)//x)+(b_(2)//y)=c_(2) Delta_(1)=|{:(a_(1),b_(1)),(a_(2),b_(2)):}|,Delta_(2)=|{:(b_(1),c_(1)),(b_(2),c_(2)):}|," "Delta_(3)=|{:(c_(1),a_(1)),(c_(2),a_(2)):}| , then (x, y) is equal to which one of the following ?