u = <-2, 1>, v = <5, 3>, find u + v

Step by step

The question

Question: find u + v, when u = ⟨−2, 1⟩ and v = ⟨5, 3⟩.

1 Draw tip to tail

Draw the grid.

Draw u from the origin.

Put the start of v at the tip of u.

Tip to tail.

The answer goes from the very start to the very end.

2 Add the parts

Add the across parts, and the up parts.

Each arrow adds its own across and up.

−2 plus 5 is 3.

1 plus 3 is 4.

So u + v = ⟨3, 4⟩.

3 Check

Let's check on the grid.

The red arrow ends at (3, 4).

That is right 3 and up 4 from the start: ⟨3, 4⟩.

The same!

Let's look back.

First: draw tip to tail.

Then: add the parts.

Last: check.