Adding Arrows

Lesson 3 of 12 · 7 min · Free, no account needed

What you will learn

To add arrows, put them tip to tail. The sum goes from the first tail to the last tip.
By parts: (a₁, a₂) + (b₁, b₂) = (a₁ + b₁, a₂ + b₂).
Order does not matter: a + b = b + a. To cancel a current, row against it.

You row straight across, but the current pushes you downstream.
Where do you land? Drag the flag on the far bank.
Row across and see.
The boat rows 4 across while the river carries it 3 along.
Put the arrows tip to tail.
Drag the loose arrow by its tail onto the tip of the other one.
That is vector addition.
To add a + b, put b's tail on a's tip. The sum runs from the first tail to the last tip.
By parts, add x with x and y with y: (0, 4) + (3, 0) = (3, 4).
Either order gives the same sum: a + b = b + a.
Add these two by parts.
Fill the sum with the chips.
Adding arrows adds their parts: (2 + 4, 5 + (-1)) = (6, 4).
Land on the dock. Lean into the current.
Drag the row arrow's head left or right. The dashed line shows where you will go.
Game: the ferry run. Three rivers, no preview.
Lean the oar and press Go. Dock on all three in as few tries as you can.
Games add arrows every frame: x = x + vx.
The sprite starts at x = 2 and vx = 3. Where is it after 3 frames?
Each frame adds the velocity arrow to the position: 2 + 3 + 3 + 3 = 11.
Which dashed arrow is a + b?
(3, 1) + (1, 3) = (4, 4). Q and R are the differences a - b and b - a.
Add arrows tip to tail. The sum is the whole trip.
Play your ferry log: every row and every current, end to end.

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