Answer:
Let [tex]\vec{A}=3\hat{i}-\hat{j}[/tex] and [tex]\vec{B}=-\hat{i}-2\hat{j}[/tex].
a)
[tex]\vec{A}+\vec{B}=(3\hat{i}-\hat{j})+(-\hat{i}-2\hat{j})=2\hat{i}-3\hat{j}[/tex]
b)
[tex]\vec{A}-\vec{B}=(3\hat{i}-\hat{j})-(-\hat{i}-2\hat{j})=4\hat{i}+\hat{j}[/tex]
c) Now we calculate the direction of [tex]\vec{A}+\vec{B}[/tex] and [tex]\vec{A}-\vec{B}[/tex]
We calculate the direction of [tex]\vec{A}+\vec{B}[/tex] like this:
[tex]\theta=tan^{-1}(\frac{-3}{2})=-56,3^{\circ}[/tex]. Since, [tex]270\leq\theta\leq360[/tex], then the direction of [tex]\vec{A}+\vec{B}[/tex] is [tex]360^{\circ}-\theta=360^{\circ}-56.3^{\circ}=303.7^{\circ}[/tex].
Now, for [tex]\vec{A}-\vec{B}[/tex]
[tex]\theta=tan^{-1}(\frac{1}{4})=14^{\circ}[/tex].
