Solve Vertex of Angles of Polygon

Use this calculate to solve angle between 2 vectors in 3D space.


The vertex is a corner of the polygon. Assuming three vertices and n-sides of polygon are given.

Steps to calculate the angle between vertices of polygons

Given vertices (12, 8, 9) and polygon sides 6

Vector Snapshot

Vectors are quantities defined by magnitude and direction. The geometrical representation of a vector is by means of an arrow whose length, to some scale, represents the magnitude of the physical quantity and whose direction indicates the direction of the vector.

A scalar quantity is one which is completely defined by its magnitude.

To distinguish the magnitude of a vector a from its direction we use the mathematical notation

Magnitude of a Vector

If the components of a vector in a rectangular coordinate system are known. To distinguish the magnitude of a vector a from its direction we use the mathematical notation. Since the vector and its components form a right-angled triangle, we have the magnitude of a vector is defined as 

Angle Between Two Vectors Calculator In 3d

Characteristics of a Unit Vector

Vectors have magnitude and direction, but if we wish to indicate the direction only we define a unit vector. A unit vector has a magnitude of 1 unit; consequently it defines the direction only.

Angle Between Two Vectors Calculator

In such a three-dimensional system, unit vectors are denoted by the letters i,j ,k.

The position vector of P has three components:
1 a component Px i along the x-axis;
2 a component Py j along the y-axis;
3 a component Pz k along the z-axis

Norm or Length of a Vector

The norm or length of a vector u in R, denoted by ||u||, and is defined to be the nonnegative square root of u.u. In particular, then

A vector |u| is called a unit vector if ||u|| = 1 or equivalently, if u.u = 1. For any nonzero vector v in Rn,  the vector

is the unique unit vector in the same direction as v. The process of finding v from v is called normalizing v.


 Suppose u = (1, -2, -4, 5, 3). Find || u ||.