Problem $1$:

Vectors vec$(A)$ and vec$(B)$ are shown in Figure $1.$

a$.$ What is vec$(A)$ in terms of $x$ and $y$ components? Answer: vec$(A)=2\mathrm{.}74$hat$()+7\mathrm{.}52$hat$()$

b$.$ What is vec$(B)$ in terms of $x$ and $y$ components? Answer: vec$(B)=-18\mathrm{.}13$hat$()-8\mathrm{.}45$hat$()$

c$.$ What is the resultant vector vec$(R)=$vec$(A)+$vec$(B)?$ Answer: vec$(R)=-15\mathrm{.}39$hat$()-0\mathrm{.}93$hat$()$

d$.$ What is $R,$ the magnitude of vec$(R)?$ Answer: $R=15\mathrm{.}42$

e$.$ What is $,$ the angle vec$(R)$ makes with respect to the $+x-$axis? $=180+3\mathrm{.}46=183\mathrm{.}46$

Figure $1$: Vectors for Problem $1.$