Use the vectors drawn at right to complete the parts below. 

1. Rewrite each vector in both component and $\mathbf{i, j}$ form.

   Partial answer (a):

   $\mathbf{\vec{A}} = -1\mathbf{i} + 3\mathbf{j}$

2. Determine each vector’s standard angle.

   Step (b):

   Solve $\tan(θ) = 3/1$. This will solve for the angle in the slope triangle for A.
   Recall that the standard angle is measured from the positive $x$-axis.

3. What are $\mathbf{\vec { A }}+\mathbf{\vec { B }}$ and $\mathbf{\vec { B }}-\mathbf{\vec { A }}$ ?

   Step (c):

   $\mathbf{\vec{A}} + \mathbf{\vec{B}} = 〈 –1, 3〉 + 〈 4, 3〉 = ?$

4. Determine $| | \mathbf{\vec { B } }| | \cdot \mathbf{\vec { A }}$.

   Hint (d):

   The double bars mean "the magnitude of". To calculate the magnitude of vector B, use the Pythagorean Theorem.