Vector
A quantity with a size and a direction, written as a list of numbers such as (3, 4). Its length is the square root of the sum of squares of its entries.
Last updated
Analogy
A set of walking directions: 3 steps east and 4 steps north.
Example
Length = sqrt(3^2 + 4^2).= sqrt(9 + 16) = sqrt(25).Length = 5.2v = (6, 8), length 10.
In practice
Vectors describe forces, velocities and data points with many features.
Practice
Flashcards
- What is the length of the vector (3, 4)?5.
Questions people ask
How do I add and scale vectors?
Add vectors entry by entry, so (1, 2) plus (3, 4) is (4, 6). To scale, multiply every entry by the number, so 2 times (3, 4) is (6, 8). Scaling by a positive number keeps the direction and changes the length. Scaling by a negative number also flips the arrow around to point the opposite way.
What is a unit vector?
A unit vector has length 1 and shows pure direction. To make one, divide a vector by its length. For (3, 4), the length is 5, so the unit vector is (3/5, 4/5), which is (0.6, 0.8). Its length is sqrt(0.36 + 0.64) = 1.