Perform the indicated vector operations.  

1. $⟨-5,7⟩+⟨3,-3⟩$ 

   Step (a):

   $⟨−5 + 3, 7 + \left(−3\right)⟩$

2. $(-7\mathbf{\text{i}}-2\mathbf{\text{j}})-2(3\mathbf{\text{i}}-\mathbf{\text{j}})$ 

3. What is the angle between $⟨-4,5⟩$ and $⟨2,7⟩$?

4. If $\vec { \text{u} }= 2\mathbf{i} – 3\mathbf{j}$ and $\vec { \text{v} }= –4\mathbf{i} – 2\mathbf{j},$ evaluate $\vec { \text{u} } · \vec{\text{v}}$. What does your answer tell you about the two vectors?

• Hint (d):

  If the dot product is positive, then the angle between the vectors is acute.