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

Let’s solve each problem step by step.

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Section A: Write the resultant column vector from the diagram.

We add vectors by adding their horizontal (x) and vertical (y) components separately.

In each diagram, we look at how far right/left (horizontal) and up/down (vertical) the total movement is from start to end of the red arrow (resultant).

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Problem 2:
Blue vector: → 2 units right, 0 up = (2, 0)
Green vector: ↑ 0 right, 3 units up = (0, 3)
Resultant: (2+0, 0+3) = (2, 3)

Wait — let me check the diagram again mentally:
Actually, in Problem 2, blue goes right 2, green goes up 3 → so yes, (2, 3)

But wait — looking back at Example 1:
Red resultant is sum of blue + green. Blue was (3,0), green was (0,2) → (3,2). Correct.

So for Problem 2:
Blue: right 2 → x=2, y=0
Green: up 3 → x=0, y=3
Sum: x=2+0=2, y=0+3=3 → (2, 3)

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Problem 3:
Blue: up 2 → (0, 2)
Green: right 2 → (2, 0)
Sum: (0+2, 2+0) = (2, 2)

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Problem 4:
Blue: right 1, up 2 → (1, 2)
Green: right 2, up 0 → (2, 0)
Sum: (1+2, 2+0) = (3, 2)

Wait — actually, looking at direction:
From start, blue goes right 1 and up 2? Let's think coordinates.

Assume starting point is origin.

Blue vector ends at (1,2)? Then green starts there and goes right 2 → ends at (3,2). So resultant is (3,2). Yes.

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Problem 5:
Blue: right 2, up 3 → (2,3)
Green: right 2, down 2 → (2,-2)
Sum: (2+2, 3 + (-2)) = (4,1)

Check: Start at (0,0), blue to (2,3), then green adds (2,-2) → ends at (4,1). Resultant: (4,1)

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Problem 6:
Blue: up 3 → (0,3)
Green: right 1, up 1 → (1,1)
Sum: (0+1, 3+1) = (1,4)

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Problem 7:
Blue: right 2 → (2,0)
Green: down 3 → (0,-3)
Sum: (2+0, 0 + (-3)) = (2, -3)

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Problem 8:
Green: down 2 → (0,-2)
Blue: left 3 → (-3,0)
Order doesn’t matter — addition is commutative.

Sum: (0 + (-3), -2 + 0) = (-3, -2)

Note: The diagram shows green first then blue? But resultant is same regardless of order.

Start at origin, go down 2 to (0,-2), then left 3 to (-3,-2). Resultant: (-3,-2)

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Problem 9:
Green: right 2, up 4 → (2,4)
Blue: right 2, down 2 → (2,-2)
Wait — no, let’s trace:

Actually, green goes from start to top: say from (0,0) to (2,4)? Then blue goes from there to (4,2)? That would be right 2, down 2 → (2,-2)

So resultant: (2+2, 4 + (-2)) = (4,2)

Alternatively, directly from start to end: right 4, up 2 → (4,2)

Yes.

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Now Section B: Draw diagrams — but since we can't draw here, and user didn’t ask to explain or teach, and options are all false, we only need to give final answers for Section A? Wait — the instruction says “solve the problem accurately” — and the worksheet has two sections.

But in Final Answer, we must provide correct answers. Since Section B requires drawing, and we’re text-based, perhaps we should compute the column vectors for Section B as well? Because the question says “Write the resultant column vector” for Section A, and for Section B it says “Draw a diagram...”, but also gives equations like (1,3)+(1,1)=?

Looking at Section B example: they show both the equation and the diagram. And the task is to draw the diagram — but since we can’t draw, maybe we should just compute the resultant column vector for each in Section B too? The user said “solve the problem accurately” — and solving means giving the answer.

Moreover, in Section B, after the equals sign, it’s blank — so likely expecting the column vector result.

Also, note: in Section B, problem 1: (3,1)+(0,2)=(3,3) — which matches the diagram.

So for consistency, I’ll compute the resultant column vectors for Section B as well.

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Section B:

Problem 2:
(1,3) + (1,1) = (1+1, 3+1) = (2,4)

Problem 3:
(0,2) + (2,2) = (0+2, 2+2) = (2,4)

Problem 4:
(4,1) + (-3,2) = (4-3, 1+2) = (1,3)

Problem 5:
(-2,-2) + (3,-1) = (-2+3, -2 + (-1)) = (1, -3)

Problem 6:
(2,-3) + (-2,1) = (2-2, -3+1) = (0, -2)

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Now, compiling all answers.

The user didn’t specify which section, but since both are part of the worksheet, and "solve the problem" likely means all parts, I'll list all.

But to be precise, let's see the structure.

Perhaps the expected output is just the answers for the numbered problems.

Since ExplainAnswer etc. are false, we skip explanations and go straight to Final Answer with all results.

But how to format? Probably list them clearly.

Final Answer should contain only the answers.

I think best to present as:

Section A:
2. (2, 3)
3. (2, 2)
4. (3, 2)
5. (4, 1)
6. (1, 4)
7. (2, -3)
8. (-3, -2)
9. (4, 2)

Section B:
2. (2, 4)
3. (2, 4)
4. (1, 3)
5. (1, -3)
6. (0, -2)

Note: Problem 1 in each section is example, so not included.

Double-check calculations:

Section A:

2. Blue: right 2, Green: up 3 → (2,3) ✓

3. Blue: up 2, Green: right 2 → (2,2) ✓

4. Blue: right 1 up 2? From grid: if blue goes from (0,0) to (1,2), green from (1,2) to (3,2) → so green is (2,0), sum (3,2) ✓

5. Blue: (2,3), Green: (2,-2) → (4,1) ✓

6. Blue: (0,3), Green: (1,1) → (1,4) ✓

7. Blue: (2,0), Green: (0,-3) → (2,-3) ✓

8. Green: (0,-2), Blue: (-3,0) → (-3,-2) ✓

9. Green: (2,4), Blue: (2,-2) → (4,2) ✓

Section B:

2. (1+1, 3+1)=(2,4) ✓

3. (0+2,2+2)=(2,4) ✓

4. (4-3,1+2)=(1,3) ✓

5. (-2+3, -2-1)=(1,-3) ✓

6. (2-2, -3+1)=(0,-2) ✓

All correct.

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. $\begin{pmatrix} 4 \\ 2 \end{pmatrix}$

Section B:
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. $\begin{pmatrix} 0 \\ -2 \end{pmatrix}$