If a = i +2 j +3 k , b =2 i +3 j +2 k and c is a vector perpendicular to b , then a ( b c ) | b c |^2 ( b c )+ a b | b |^2 b + a c | c |^2 =

Step-by-step solution

Any vector r can be written in linear combination of two non-parallel vector b and c , as r = ( r b | b |^2 ) b + ( r c | c |^2 ) c + ( r ( b c ) | b c |^2 )( b c ) So, r = a | r |=| a |= 1+4+9 = 14 .