The value of , so that the volume of the parallelopiped formed by i + j + k , j + k and i + k becomes maximum, is

Step-by-step solution

Volume of parallelopiped is [ a b c ] aligned V & = | array ccc 1 & & 1 0 & 1 & & 0 & 1 array | & =1- (- ^2 )- & =1+ ^3- aligned Differentiating w.r.t. , we get aligned & dV d =3 ^2-1 & d ^2 ~V ~d ^2 =6 & Let dV d =0 & 3 ^2-1=0 & = 1 3 & at = -1 3 , & d ^2 ~V ~d ^2 = -6 3 < 0 aligned V is maximum at = -1 3