The force on an object is F = 15 j. For the vector v = 5 i4j, find: The component of F parallel to v: Solution The component of F parallel to v (Fv)is given by F.v\' where v\' is the unit vector along v v\'= v/|v| |v|=sqrt(25+16)=sqrt(41) Fv= (F.v)/|v|= -15*-4/sqrt(41)= 60/sqrt(41) so, the component= Fv v\' = 60/sqrt(41) (5i-4j)/sqrt(41) =60(5i-4j)/41.

1. The force on an object is F = 15 j. For the vector v = 5 i4j, find:
The component of F parallel to v:
Solution
The component of F parallel to v (Fv)is given by F.v' where v' is the unit vector
along v v'= v/|v| |v|=sqrt(25+16)=sqrt(41) Fv= (F.v)/|v|= -15*-4/sqrt(41)= 60/sqrt(41) so, the
component= Fv v' = 60/sqrt(41) (5i-4j)/sqrt(41) =60(5i-4j)/41