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The length of a vector

A vector in the plane has coordinates and a length. The length is the distance from the start of the arrow to its end, and it is found with Pythagoras. The vector from one point to another is found by subtracting the coordinates. The length of that vector is the distance between the points. A vector and the opposite vector have the same length.

Try it yourself

Vector addition

∣[x,y]∣=x2+y2|[x, y]| = \sqrt{x^2 + y^2}length
AB→=[x2−x1, y2−y1]\overrightarrow{AB} = [x_2 - x_1,\ y_2 - y_1]vector between two points

Symbols

x, yx,\ ythe coordinates

Example

The length of [3,4][3, 4] is 9+16=5\sqrt{9 + 16} = 5. From A(1,4)A(1, 4) to B(5,7)B(5, 7) the vector is [4,3][4, 3], and the length is also 55.

Subtract end minus start. If you swap the order, the vector points the other way.
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Part of Mathematics R1: Vectors in the plane.