SOLUTION: Vector addition worksheet - Studypool - Free Printable

It looks like you've uploaded a Vector Addition Worksheet with several vector pairs to add graphically. The goal is to add each pair of vectors using the head-to-tail method, then draw the resultant vector (R) as a dotted line with an arrowhead from the tail of the first vector to the head of the second.

Let’s go through each box systematically and explain how to solve them correctly, since some have been partially worked on but may need correction or clarification.

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🔷 Understanding Vector Addition

To add two vectors:
1. Place the tail of the second vector at the head of the first.
2. Draw a dotted line from the tail of the first vector to the head of the second — this is the resultant (R).
3. If the vectors cancel out completely, write "no R".

We’ll analyze each box in order.

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## ✔ Box 1: Example
- Two vectors: one upward, one rightward.
- Correctly shown: place tail of horizontal vector at head of vertical vector.
- Resultant drawn as dotted diagonal → Correct!

✔ Good example.

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## 🔹 Box 2: Top-right (First row, right column)
- Two vectors pointing down-left and up-right.
- They appear to be equal in magnitude and opposite in direction? Let's check:
- One vector points down-left (southwest), other up-right (northeast).
- If they are equal in length and opposite in direction → they cancel.

But looking closely:
- The red and blue vectors seem to be equal in magnitude and opposite in direction → their sum is zero.

➡️ Resultant = no R

⚠️ However, there is a dotted line labeled “R” drawn — that’s incorrect if vectors are equal and opposite.

✔ Correction: Write "no R" — because the vectors cancel.

> 💡 Tip: If vectors are equal and opposite, resultant is zero.

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## 🔹 Box 3: Middle-left (Second row, left column)
- One vector pointing right, another pointing down-left.
- Red vector: drawn from origin to right.
- Blue vector: starts at head of red vector and goes down-left.
- Dotted line connects tail of red to head of blue → correct.

✔ This appears to be done correctly.

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## 🔹 Box 4: Middle-right (Second row, right column)
- Two vertical vectors: one up, one down.
- Both same length?
- Upward vector has label “2”, downward has “2” → so equal magnitude.
- Same direction? No — opposite directions.
- So: 2 up + 2 down = 0

➡️ Resultant = no R

✘ But someone drew a red upward vector and a blue upward vector — this is wrong.

❗ Correction: Since both are vertical and equal in magnitude but opposite in direction, they cancel.

✔ Answer: "no R"

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## 🔹 Box 5: Third row, left column
- Two vectors pointing to the right.
- Both in the same direction → they add together.
- Red vector: placed from origin to right.
- Blue vector: placed at head of red, continues right.
- Dotted line from start to end → correct.

✔ This is correct. Resultant is longer than either vector, pointing right.

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## 🔹 Box 6: Third row, right column
- One vector pointing left (labeled 1.5), one pointing down-left (labeled 1.3)?
- Wait: labels are 1.5 and 1.3? Possibly magnitudes?

But let’s see:
- First vector: horizontal left (1.5 units).
- Second vector: diagonal down-left (1.3 units).

Now, we need to add them:
1. Place tail of second vector at head of first.
2. Draw resultant from tail of first to head of second.

The drawing shows:
- Red vector: horizontal left (1.5)
- Blue vector: from head of red, going down-left (1.3)
- Dotted line from origin to end of blue vector → this is correct.

✔ Looks good. Resultant is diagonally down-left.

Note: Magnitude not needed unless specified — just direction and construction matter.

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## 🔹 Box 7: Bottom-left (Fourth row, left column)
- Three vectors? Wait — only two should be added per box.
- But here we see:
- One right vector,
- One down vector,
- One up-right vector?

Wait — look carefully:

Actually, it seems like:
- Left side: three vectors shown, but likely only two are meant to be added.

But the box has:
- A right vector,
- A down vector,
- And a diagonally up-right vector?

No — actually, the left side shows three vectors, but the right side has a drawing.

Wait — re-examining:

The left side shows:
- One vector pointing right,
- One pointing down,
- One pointing up-right?

But the instruction says: Add each pair — so probably only two vectors per box.

Looking at the drawing on the right:
- Red vector: right
- Blue vector: down
- Then a resultant from tail of red to head of blue → forming a right triangle

So the two vectors being added are:
- Right (red)
- Down (blue)

Then resultant is diagonal down-right.

✔ This is correct — head-to-tail method used properly.

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## 🔹 Box 8: Bottom-right (Fourth row, right column)
- Two vectors:
- One pointing up-left (labeled 2.7),
- One pointing down (labeled 1.3)
- We must add them.

Steps:
1. Place tail of second vector at head of first.
2. Draw resultant from tail of first to head of second.

In the drawing:
- Red vector: up-left (2.7)
- Blue vector: starts at head of red, goes down (1.3)
- Dotted line from tail of red to head of blue → this is correct

✔ This is correct. Resultant is slightly down-left.

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✔ Summary of Corrections & Answers

| Box | Vectors | Resultant | Comment |
|-----|--------|-----------|--------|
| 1 | ↑, → | ↗ (dotted) | Correct (example) |
| 2 | ←↓, →↑ | no R | Equal and opposite → cancel |
| 3 | →, ↘ | ↘ (dotted) | Correct |
| 4 | ↑, ↓ | no R | Equal and opposite → cancel |
| 5 | →, → | →→ (longer) | Correct |
| 6 | ←, ↙ | ↙ (dotted) | Correct |
| 7 | →, ↓ | ↘ (dotted) | Correct |
| 8 | ↖, ↓ | ↙ (dotted) | Correct |

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🛠 Final Recommendations:

1. Box 2: Remove dotted line, write "no R"
2. Box 4: Remove red/blue lines, write "no R"
3. All others are correct.

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✔ How to Add Vectors Graphically:

1. Head-to-Tail Method:
- Move the second vector so its tail touches the head of the first.
- Draw resultant from tail of first to head of second.
2. Use dotted line for resultant.
3. If vectors cancel → write "no R".

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Let me know if you want me to draw these corrections digitally or provide a step-by-step guide for any specific box!