If the volume of the parallelopiped whose conterminus edges are along the vectors a , b , c is 12, then the volume of the tetrahedron whose conterminus edges are a + b , b + c and c + a is

Step-by-step solution

(C) Volume of parallelepiped =[ a b c ]=12 [ array lll a & b & c array ]=12 (1) volume of tetrahedrom = 1 6 [ array lll a + b & b + c & c + a array ]= 1 6 ( a + b ) [( b + c ) ( c + a )]= 1 6 ( a + b ) [( b c )+( b a )+( c c )+( c a )]= 1 6 a ( b c )+ a ( b a )+ a ( c a )+ b ( b c )+ b ( b a )+ b ( c a ) [ c c =0]= 1 6 [ a ( b c )+0+ b ( c a )]= 1 6 [ a b c ]+[ a b c ] = 2 6 [ a b c ]= 1 3 (12)=4