It looks like you've uploaded an image with several vector-related problems. Let's go over them step by step. Here's a quick breakdown of the questions from the image:

1. Problem 1 (Vector operations and plotting):

   • Vectors: $\mathbf{a} = 2i - j$, $\mathbf{b} = -2i + 3j$, $\mathbf{c} = 4i + j$
   • Required to calculate: $\mathbf{a} + \mathbf{b}$, $\mathbf{a} - \mathbf{c}$, $2\mathbf{b} - \mathbf{a}$, and $|\mathbf{a} + \mathbf{b}|$
   • Plot vectors $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$, $\mathbf{a} + \mathbf{b}$, $\mathbf{a} - \mathbf{c}$ in the x, y plane.

2. Problem 2 (Solving for unknowns):

   • Vectors: $\mathbf{p} = 3i + uj$, $\mathbf{q} = vi - 4j$, $\mathbf{r} = 4i - 6j$
   • Solve for $u$ and $v$ if $\mathbf{p} - \mathbf{q} = \mathbf{r}$
   • Find $u$ if $\mathbf{p}$ and $\mathbf{r}$ are parallel.

3. Problem 3 (Vector magnitudes and directions):

   • Given $\mathbf{a} = -3i + 4j$
   • Find a vector parallel to $\mathbf{a}$ with magnitude 20.
   • Find a unit vector in the direction of $\mathbf{a}$.

4. Problem 4 (Component form of vectors):

   • Express the given vectors in the form $\mathbf{a} = a_1i + a_2j$ for different magnitudes and directions from the diagrams.

5. Problem 5 (Magnitude and direction of vectors):

   • Find magnitude and direction $\theta$ of several vectors.

6. Problem 6 (Vector operations in 3D):

   • Vectors: $\mathbf{a} = 3i - j + 2k$, $\mathbf{b} = 6i - 3j - 2k$, $\mathbf{c} = i + j - 3k$
   • Perform vector operations and find magnitudes, angles, and parallel vectors.

Would you like me to start by solving a specific problem, or provide step-by-step explanations for one of the sections? Feel free to guide me!