The image shows a worksheet where you are asked to solve vector combinations graphically. The problems listed seem to require vector addition and subtraction, and each graphical solution shows arrows representing the vectors and their sums or differences.

Here’s a breakdown of the problems:

Problem 9: $A + B$

• You are adding vector $A$ to vector $B$.
• Graphically, this involves placing the tail of $B$ at the head of $A$.
• The resulting vector $R$ is the one from the tail of $A$ to the head of $B$.

Problem 10: $B - C$

• Subtracting vectors means adding the opposite of $C$. So, $B - C$ is the same as $B + (-C)$.
• The vector $-C$ is in the opposite direction of $C$.
• $B$ and $-C$ are placed head to tail, and the resultant vector $R$ is from the tail of $B$ to the head of $-C$.

Problem 11: $A + 2B + C$

• You add $A$, two times $B$ (so it should be a longer vector), and $C$.
• Start with $A$, then place two $B$ vectors one after the other, and finally add $C$.
• The resultant $R$ is from the tail of $A$ to the head of $C$.

Problem 12: $A - \frac{1}{2}C$

• This involves subtracting half of $C$, which is equivalent to adding $-\frac{1}{2}C$.
• The vector $-\frac{1}{2}C$ points in the opposite direction to $C$ and has half the length.
• The resultant vector is from the tail of $A$ to the head of $-\frac{1}{2}C$.

It appears that the student made errors in some of the graphical representations (notably problem 10), and the corrections in red ink suggest improvements in the diagrams.

Do you want more detailed steps on how to graphically add or subtract these vectors? Let me know if you have any questions.

Here are 5 relative questions for further practice:

1. How would you graphically represent $A - B$?
2. How would you change the graphical representation if vector $C$ were twice as long?
3. What happens to the resultant vector when you subtract instead of add vectors?
4. Can you explain how scalar multiplication (like $2B$) affects the graphical representation of a vector?
5. What does it mean geometrically when two vectors cancel each other out (i.e., sum to zero)?

Tip: When adding vectors graphically, always ensure that the head of one vector touches the tail of the next to maintain accuracy.