In this problem we are going to consider two different examples of the dot product between two vectors, a force vec$(F)$ and a displacement vec$(r).$

Part $($a$)$

If the force vector has a magnitude of $F=19N,$ the displacement has a length of $r=0\mathrm{.}95m,$ and the angle between the vectors is $45,$ what will the dot product between vec$(F)$ and the vector vec$(r)$ be$?$ Your answer should be in joules $($which is the same as newton$-$meters$).$

vec$(F)*vec(r)=$

$$ J

Part $($b$)$

If the force vector has components $F_x=5\mathrm{.}5N$ and $F_y=14\mathrm{.}8N,$ and the displacement vector has components $r_x=0\mathrm{.}45m$ and $r_y=0\mathrm{.}67m,$ what is the dot product between them? Enter your answer in joules.