104. If a, b, c and a’, b’, c’ are such that
a’• a = b’• b = c’• c = 1
a’• b = a’• c = b’• a = b’• c = c’• a = c’ • b =0
Prove that it necessarily follows that
a^'= (b x c)/(a• bxc) , b^'= cxa/(a•bxc) ,
c^'= axb/(a•bxc)
Show that a necessary and suffiecient condition that the vectors
A= A1i + A2j +A3k,
B=B1i + B2j + B3k,
C= C1i + C2j + C3k
be linearly independent is that the determinant |(A1&A2&A3@B1&B2&B3@C1&C2&C3)| be different from zero.