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

Problem Overview:

The task involves solving vector addition problems in two sections:
1. Section A: Given diagrams of vectors, determine the resultant column vector.
2. Section B: Given column vectors, perform their addition and draw the resultant vector.

Solution:

#### Section A: Diagrams to Resultant Column Vectors

In this section, we need to analyze each diagram and determine the resultant vector by summing the horizontal and vertical components of the vectors shown.

##### Example (Already Solved):
- The diagram shows a vector moving 3 units right and 2 units up.
- The resultant column vector is:
\[
\begin{pmatrix} 3 \\ 2 \end{pmatrix}
\]

##### Problem 1:
- The vector moves 2 units right and 1 unit up.
- Resultant column vector:
\[
\begin{pmatrix} 2 \\ 1 \end{pmatrix}
\]

##### Problem 2:
- The vector moves 1 unit right and 3 units up.
- Resultant column vector:
\[
\begin{pmatrix} 1 \\ 3 \end{pmatrix}
\]

##### Problem 3:
- The vector moves 2 units right and 1 unit up.
- Resultant column vector:
\[
\begin{pmatrix} 2 \\ 1 \end{pmatrix}
\]

##### Problem 4:
- The vector moves 3 units right and 1 unit up.
- Resultant column vector:
\[
\begin{pmatrix} 3 \\ 1 \end{pmatrix}
\]

##### Problem 5:
- The vector moves 2 units right and 2 units down.
- Resultant column vector:
\[
\begin{pmatrix} 2 \\ -2 \end{pmatrix}
\]

##### Problem 6:
- The vector moves 1 unit right and 3 units up.
- Resultant column vector:
\[
\begin{pmatrix} 1 \\ 3 \end{pmatrix}
\]

##### Problem 7:
- The vector moves 2 units right and 2 units down.
- Resultant column vector:
\[
\begin{pmatrix} 2 \\ -2 \end{pmatrix}
\]

##### Problem 8:
- The vector moves 3 units left and 2 units down.
- Resultant column vector:
\[
\begin{pmatrix} -3 \\ -2 \end{pmatrix}
\]

##### Problem 9:
- The vector moves 3 units right and 2 units down.
- Resultant column vector:
\[
\begin{pmatrix} 3 \\ -2 \end{pmatrix}
\]

#### Section B: Column Vector Addition and Diagrams

In this section, we add the given column vectors and then draw the resultant vector.

##### Example (Already Solved):
- Add:
\[
\begin{pmatrix} 3 \\ 1 \end{pmatrix} + \begin{pmatrix} 0 \\ 2 \end{pmatrix} = \begin{pmatrix} 3+0 \\ 1+2 \end{pmatrix} = \begin{pmatrix} 3 \\ 3 \end{pmatrix}
\]
- Draw the resultant vector: Move 3 units right and 3 units up.

##### Problem 1:
- Add:
\[
\begin{pmatrix} 3 \\ 1 \end{pmatrix} + \begin{pmatrix} 0 \\ 2 \end{pmatrix} = \begin{pmatrix} 3+0 \\ 1+2 \end{pmatrix} = \begin{pmatrix} 3 \\ 3 \end{pmatrix}
\]
- Draw the resultant vector: Move 3 units right and 3 units up.

##### Problem 2:
- Add:
\[
\begin{pmatrix} 1 \\ 3 \end{pmatrix} + \begin{pmatrix} 1 \\ 1 \end{pmatrix} = \begin{pmatrix} 1+1 \\ 3+1 \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}
\]
- Draw the resultant vector: Move 2 units right and 4 units up.

##### Problem 3:
- Add:
\[
\begin{pmatrix} 0 \\ 2 \end{pmatrix} + \begin{pmatrix} 2 \\ 2 \end{pmatrix} = \begin{pmatrix} 0+2 \\ 2+2 \end{pmatrix} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}
\]
- Draw the resultant vector: Move 2 units right and 4 units up.

##### Problem 4:
- Add:
\[
\begin{pmatrix} 4 \\ 1 \end{pmatrix} + \begin{pmatrix} -3 \\ 2 \end{pmatrix} = \begin{pmatrix} 4+(-3) \\ 1+2 \end{pmatrix} = \begin{pmatrix} 1 \\ 3 \end{pmatrix}
\]
- Draw the resultant vector: Move 1 unit right and 3 units up.

##### Problem 5:
- Add:
\[
\begin{pmatrix} -2 \\ -2 \end{pmatrix} + \begin{pmatrix} 3 \\ -1 \end{pmatrix} = \begin{pmatrix} -2+3 \\ -2+(-1) \end{pmatrix} = \begin{pmatrix} 1 \\ -3 \end{pmatrix}
\]
- Draw the resultant vector: Move 1 unit right and 3 units down.

##### Problem 6:
- Add:
\[
\begin{pmatrix} 2 \\ -3 \end{pmatrix} + \begin{pmatrix} -2 \\ 1 \end{pmatrix} = \begin{pmatrix} 2+(-2) \\ -3+1 \end{pmatrix} = \begin{pmatrix} 0 \\ -2 \end{pmatrix}
\]
- Draw the resultant vector: Move 0 units right and 2 units down.

Final Answers:

#### Section A:
1. \(\begin{pmatrix} 2 \\ 1 \end{pmatrix}\)
2. \(\begin{pmatrix} 1 \\ 3 \end{pmatrix}\)
3. \(\begin{pmatrix} 2 \\ 1 \end{pmatrix}\)
4. \(\begin{pmatrix} 3 \\ 1 \end{pmatrix}\)
5. \(\begin{pmatrix} 2 \\ -2 \end{pmatrix}\)
6. \(\begin{pmatrix} 1 \\ 3 \end{pmatrix}\)
7. \(\begin{pmatrix} 2 \\ -2 \end{pmatrix}\)
8. \(\begin{pmatrix} -3 \\ -2 \end{pmatrix}\)
9. \(\begin{pmatrix} 3 \\ -2 \end{pmatrix}\)

#### Section B:
1. \(\begin{pmatrix} 3 \\ 3 \end{pmatrix}\)
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. \(\begin{pmatrix} 0 \\ -2 \end{pmatrix}\)

\(\boxed{\text{See detailed solutions above}}\)