If the volume of the parallelopiped formed by three non-coplanar vectors a , b and c is 4 cu units, then [ a b b c c a ] is equal to

Step-by-step solution

In scalar triple product, the position of dot and cross can be changed provided the cyclic order is maintained i.e., [ a b c ]=( a b ) c = a ( b c ) Put c a = n [ a b b c c a ]=( a b ) ( b c ) n =( a b ) ( n b ) c -( n c ) b =( a b ) [ ( c a ) b c - ( c a ) c b ]=( a b ) [ c a b ] c -[ c a c ] b =[( a b ) c ][ c a b ]-0=[ a b c ] [abc] =[ a b c ]²=(4)²=16 Alternate Method By properties of Scalar triple product, [ a b b c c a ]= [ array lll a & b & c ² array . =(4)²=16