If a , b , c are nonzero vectors along the coterminus edges of a parallelopiped with volume 7 cubic units, then the volume of a parallelopiped with a + b , b + c , c + a as the coterminus edges is

Step-by-step solution

(A) We have [ a ( b c )]=7[ a + b b + c c + a ]=( a + b ) [( b + c ) ( c + a )]=( a + b ) [( b c )+( b a )+( c c )+( c a )]=[ a ( b c )]+[ a ( b a )]+[ a ( c a )]+[ b ( b c )]+[ b ( b a )]+[ b ( c a )]=[ a ( b c )]+0+[ b ( c a )]=[ a ( b c )]+[ a ( b c )]=2[ a ( b c )]=2(7)=14