Vectors · SumNinja

Vector addition practice

Add two-dimensional vectors by combining their horizontal and vertical parts.

2-minute Session · Free · No sign-up

Try a warm-up

Take your time. You can try again.

Add the two moves. Where do you end up?

\begin{bmatrix}2\\1\end{bmatrix}+\begin{bmatrix}-1\\3\end{bmatrix}=?

Get a hint

Add top to top, then bottom to bottom.

Choose an answer when you’re ready.

See the answer and why

$\begin{bmatrix}1\\4\end{bmatrix}$

Add the top numbers: 2 + (−1) = 1. Add the bottom numbers: 1 + 3 = 4.

Your next round

A short, 2-minute Session
Tap a choice or type your answer
Review your answers in Progress

How Vectors practice works

A vector describes a move with both size and direction. In a column vector, the top number gives the horizontal move. The bottom number gives the vertical move. Positive numbers move right or up; negative numbers move left or down.

Add matching parts

Suppose one move takes you 2 steps right and 1 up. A second move takes you 1 left and 3 up. Together, they take you 1 right and 4 up. Add the top numbers, then add the bottom numbers.

See how it works

(2, 1) + (−1, 3) = (1, 4)

Horizontal: 2 + (−1) = 1. Vertical: 1 + 3 = 4. Keep the two parts in the same order.

3 × (2, −1) = (6, −3)

Scaling repeats the whole move. Multiply both parts by 3: six steps right and three down.

The first button starts with addition. The lessons below also show how to subtract or scale vectors, find a move between points, measure length, and use a dot product. Their practice links let you try each skill. These activities use 2D vectors.