**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.

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

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

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

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.

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

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

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

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