Column Vector Addition Free Worksheet | Fun and Engaging PDF ... - Free Printable

Here are the solutions for the Column Vector Addition worksheet.

Section A: Write the resultant column vector

*To find the answer, count how many squares the blue arrow goes across (left/right) and up/down, then do the same for the green arrow. Add the horizontal numbers together and the vertical numbers together.*

2.
* Blue vector: 2 right, 0 up $\rightarrow \begin{pmatrix} 2 \\ 0 \end{pmatrix}$
* Green vector: 0 right, 3 up $\rightarrow \begin{pmatrix} 0 \\ 3 \end{pmatrix}$
* Total: $2+0=2$ and $0+3=3$
* Answer: $\begin{pmatrix} 2 \\ 3 \end{pmatrix}$

3.
* Blue vector: 0 right, 2 up $\rightarrow \begin{pmatrix} 0 \\ 2 \end{pmatrix}$
* Green vector: 2 right, 0 up $\rightarrow \begin{pmatrix} 2 \\ 0 \end{pmatrix}$
* Total: $0+2=2$ and $2+0=2$
* Answer: $\begin{pmatrix} 2 \\ 2 \end{pmatrix}$

4.
* Blue vector: 1 right, 2 up $\rightarrow \begin{pmatrix} 1 \\ 2 \end{pmatrix}$
* Green vector: 2 right, 0 up $\rightarrow \begin{pmatrix} 2 \\ 0 \end{pmatrix}$
* Total: $1+2=3$ and $2+0=2$
* Answer: $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$

5.
* Blue vector: 2 right, 3 up $\rightarrow \begin{pmatrix} 2 \\ 3 \end{pmatrix}$
* Green vector: 2 right, 2 down $\rightarrow \begin{pmatrix} 2 \\ -2 \end{pmatrix}$
* Total: $2+2=4$ and $3+(-2)=1$
* Answer: $\begin{pmatrix} 4 \\ 1 \end{pmatrix}$

6.
* Blue vector: 0 right, 3 up $\rightarrow \begin{pmatrix} 0 \\ 3 \end{pmatrix}$
* Green vector: 1 right, 1 up $\rightarrow \begin{pmatrix} 1 \\ 1 \end{pmatrix}$
* Total: $0+1=1$ and $3+1=4$
* Answer: $\begin{pmatrix} 1 \\ 4 \end{pmatrix}$

7.
* Blue vector: 2 right, 0 up $\rightarrow \begin{pmatrix} 2 \\ 0 \end{pmatrix}$
* Green vector: 0 right, 3 down $\rightarrow \begin{pmatrix} 0 \\ -3 \end{pmatrix}$
* Total: $2+0=2$ and $0+(-3)=-3$
* Answer: $\begin{pmatrix} 2 \\ -3 \end{pmatrix}$

8.
* Blue vector: 3 left, 0 up $\rightarrow \begin{pmatrix} -3 \\ 0 \end{pmatrix}$
* Green vector: 0 right, 2 down $\rightarrow \begin{pmatrix} 0 \\ -2 \end{pmatrix}$
* Total: $-3+0=-3$ and $0+(-2)=-2$
* Answer: $\begin{pmatrix} -3 \\ -2 \end{pmatrix}$

9.
* Blue vector: 2 right, 2 down $\rightarrow \begin{pmatrix} 2 \\ -2 \end{pmatrix}$ *(Note: The arrow points from top-left to bottom-right)*
* Green vector: 2 left, 4 down $\rightarrow \begin{pmatrix} -2 \\ -4 \end{pmatrix}$ *(Note: The arrow points from top-right to bottom-left)*
* Total: $2+(-2)=0$ and $-2+(-4)=-6$
* Answer: $\begin{pmatrix} 0 \\ -6 \end{pmatrix}$

---

Section B: Draw a diagram

*First, calculate the sum of the numbers. Then, on the grid, draw an arrow starting from a point that moves according to your answer (Right/Left for the top number, Up/Down for the bottom number).*

2.
* Calculation: $\begin{pmatrix} 1 \\ 3 \end{pmatrix} + \begin{pmatrix} 1 \\ 1 \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$
* Draw: An arrow going 2 squares Right and 4 squares Up.

3.
* Calculation: $\begin{pmatrix} 0 \\ 2 \end{pmatrix} + \begin{pmatrix} 2 \\ 2 \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$
* Draw: An arrow going 2 squares Right and 4 squares Up.

4.
* Calculation: $\begin{pmatrix} 4 \\ 1 \end{pmatrix} + \begin{pmatrix} -3 \\ 2 \end{pmatrix} = \begin{pmatrix} 1 \\ 3 \end{pmatrix}$
* Draw: An arrow going 1 square Right and 3 squares Up.

5.
* Calculation: $\begin{pmatrix} -2 \\ -2 \end{pmatrix} + \begin{pmatrix} 3 \\ -1 \end{pmatrix} = \begin{pmatrix} 1 \\ -3 \end{pmatrix}$
* Draw: An arrow going 1 square Right and 3 squares Down.

6.
* Calculation: $\begin{pmatrix} 2 \\ -3 \end{pmatrix} + \begin{pmatrix} -2 \\ 1 \end{pmatrix} = \begin{pmatrix} 0 \\ -2 \end{pmatrix}$
* Draw: An arrow going 0 squares sideways and 2 squares Down (a straight vertical line pointing down).

Final Answer:
Section A:
2. $\begin{pmatrix} 2 \\ 3 \end{pmatrix}$
3. $\begin{pmatrix} 2 \\ 2 \end{pmatrix}$
4. $\begin{pmatrix} 3 \\ 2 \end{pmatrix}$
5. $\begin{pmatrix} 4 \\ 1 \end{pmatrix}$
6. $\begin{pmatrix} 1 \\ 4 \end{pmatrix}$
7. $\begin{pmatrix} 2 \\ -3 \end{pmatrix}$
8. $\begin{pmatrix} -3 \\ -2 \end{pmatrix}$
9. $\begin{pmatrix} 0 \\ -6 \end{pmatrix}$

Section B (Resultant Vectors to Draw):
2. $\begin{pmatrix} 2 \\ 4 \end{pmatrix}$
3. $\begin{pmatrix} 2 \\ 4 \end{pmatrix}$
4. $\begin{pmatrix} 1 \\ 3 \end{pmatrix}$
5. $\begin{pmatrix} 1 \\ -3 \end{pmatrix}$
6. $\begin{pmatrix} 0 \\ -2 \end{pmatrix}$