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, based on the directions and the example provided.

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🔷 Understanding Vector Addition (Head-to-Tail Method):

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".

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We’ll analyze each box one by one:

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✔ Box 1 (Top Left - Example)

- Two vectors: one pointing up, one pointing right.
- Resultant drawn correctly as a diagonal from origin to the end of the second vector (using head-to-tail).
- ✔️ Correctly shown with dotted line and arrowhead labeled R.

✔ This is a correct example.

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🟨 Box 2 (Top Right)

- Vectors: One pointing down-left, one pointing up-right.
- The student has drawn a blue vector (first), then red (second), connected head-to-tail.
- Dotted line from start of first to end of second → shows R.
- But let's check: are they equal in magnitude and opposite? Not exactly — they seem to be similar but not identical.
- The resultant appears to be short and angled, which makes sense if they partially cancel.

✔ Looks correct — the addition is done properly.

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🟨 Box 3 (Middle Left)

- Vectors: One pointing right, one pointing down-left.
- Student drew red vector (right), then purple vector (down-left), connected head-to-tail.
- Dotted line from start of red to end of purple → R.
- The direction of R is down-right, which is correct.

✔ Correct — proper head-to-tail addition.

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🟨 Box 4 (Middle Right)

- Vectors: One pointing down, one pointing up — both vertical.
- The down vector is labeled “2”, up vector is labeled “2” — same magnitude, opposite direction.
- So: 2 down + 2 up = 0 → They cancel!
- Resultant should be "no R".

✘ Mistake here: The student drew a red and blue vector and added a resultant (R).
But since they are equal and opposite, the net result is zero.

🟢 Correction: Write "no R" in this box.

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🟨 Box 5 (Bottom Left)

- Vectors: Two pointing right, one pointing down-left.
- Wait — there are three vectors shown? But instructions say “pair of vectors”.

Wait — looking closely: There are two vectors in the left side: one right, one down-left.

So:
- First vector: → (right)
- Second vector: ↘ (down-left)

Student draws red →, then purple ↘, connects head-to-tail.
Then draws dotted line from start to end → R.

✔ This is correct — the resultant is diagonally down-right.

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🟨 Box 6 (Bottom Right)

- Vectors: One pointing left, one pointing down.
- Labeled: “2.7” (left), “1.3” (down).
- These are not equal or opposite — so they don’t cancel.
- Student drew red (left), then purple (down), connected head-to-tail.
- Then drew dotted line from start to end → R.

✔ Correct — resultant points down-left, magnitude calculated via Pythagoras would be √(2.7² + 1.3²) ≈ 3.0, angle ~25° below horizontal.

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🟨 Box 7 (Bottom Left – Below Box 5)

- Three vectors shown? Let’s see:
- One → (right)
- One ↓ (down)
- One ↘ (down-right)

But again, the instruction says “each pair” — so likely only two vectors per box.

Looking at the layout: It seems the last row has three boxes, but only two are filled?

Actually, it appears that the bottom-left box (below Box 5) has three vectors drawn, but the task is to add pairs.

Wait — perhaps this is a typo or misalignment.

But in the image, the bottom-left box shows:
- A vector →
- A vector ↓
- A vector ↘

But the student drew:
- Red →
- Blue ↓
- Then a red diagonal → R

This suggests they're adding → + ↓ → ↘

So they’re doing: Right + Down = Diagonal down-right

That’s valid.

✔ Correct — the resultant is the diagonal from origin to end of the second vector.

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🟨 Box 8 (Bottom Right – Last Box)

- Two vectors: one pointing up-left, one pointing down.
- Labeled: “2.7” (up-left), “1.3” (down).
- Student drew red (up-left), then blue (down), connected head-to-tail.
- Then dotted line from start to end → R.

✔ Correct — the resultant will be shorter than either, depending on angles.

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✘ Summary of Errors

The only incorrect box is Box 4 (Middle Right).

> Box 4: Two vertical vectors — one down (2), one up (2). They are equal in magnitude, opposite in direction → Net force = 0 → Resultant = no R

✘ But student drew a resultant (R). That’s wrong.

🟢 Fix: In that box, erase the resultant and write "no R".

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✔ Final Answer & Corrections:

| Box | Vectors | Resultant | Correction Needed? |
|-----|--------|----------|-------------------|
| 1 | ↑, → | ↗ | No |
| 2 | ↙, ↗ | Short ↘ | No |
| 3 | →, ↙ | ↘ | No |
| 4 | ↓ (2), ↑ (2) | no R | ✘ YES — write "no R" |
| 5 | →, ↘ | ↘ | No |
| 6 | ← (2.7), ↓ (1.3) | ↙ | No |
| 7 | →, ↓ | ↘ | No |
| 8 | ↖ (2.7), ↓ (1.3) | ↙ | No |

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✔ How to Fix the Worksheet:

1. In Box 4 (Middle Right), erase the red and blue vectors and the resultant.
2. Write "no R" in that box.
3. All other boxes are correctly solved.

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💡 Tip for Future:

When adding vectors:
- Opposite and equal vectors cancel → no R
- Use head-to-tail method carefully.
- Always draw the resultant from tail of first to head of last.

Let me know if you'd like a digital version of the corrected worksheet!