When you add two vectors tip to tail, where do you draw the second vector?

Starting at the middle of the first vector

Starting at the tip of the first vector

Starting from the same point as the first vector

With the parallelogram rule, which line is the resultant vector?

The diagonal joining the tips of the two vectors

One of the sides of the parallelogram

The diagonal from the shared starting point to the opposite corner

Does adding the first vector to the second give the same result as adding the second to the first?

Yes, the order does not change the resultant

Only if both vectors have the same length

No, the resultant points in a different direction

Adding two vectors by drawing

Age 15 · Maths

Open to everyone until Friday, October 30

To keep it, print it while it is open.

To add two vectors, draw the second one starting at the tip of the first, then draw an arrow from the very start to the final tip. You get the same result if you draw both from one point, complete a parallelogram, and follow its diagonal.

In the picture

First vector: the red arrow, with its own length and direction
Second vector: the blue arrow, starting from the same point
Copy of the second vector placed tip to tail on the head of the first
Resultant vector: the diagonal from the shared start to the opposite corner

Examples

A swimmer heads straight across a river while the current pushes them sideways, so they actually move along a slanted path.
Two people pull a sled with ropes at different angles, and the sled slides in the direction of the combined pull.

Key takeaways

Tip to tail and the parallelogram rule always give the same resultant vector.
The order doesn’t matter: the first vector plus the second equals the second plus the first.

Quiz: Adding two vectors by drawing (Age 15)

1
When you add two vectors tip to tail, where do you draw the second vector?
- Starting at the middle of the first vector
- Starting at the tip of the first vector
- Starting from the same point as the first vector
2
With the parallelogram rule, which line is the resultant vector?
- The diagonal joining the tips of the two vectors
- One of the sides of the parallelogram
- The diagonal from the shared starting point to the opposite corner
3
Does adding the first vector to the second give the same result as adding the second to the first?
- Yes, the order does not change the resultant
- Only if both vectors have the same length
- No, the resultant points in a different direction

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Maths, Age 15