# 3# Force Vector (3D)

## Cartesian Vector 3D to solve Force Vector 3D

#### Right Hand Coordinate System

A rectangular coordinate system is said to be right-handed if the thumb of the right hand points in the direction of the positive Z axis when the right-hand fingers are curled about this axis and directed from the positive x-axis towards the positive y-axis.

#### Rectangular Components of a Force vector 3D

**A = A _{X }+ A_{Y} + A_{Z}**

**A’ = A _{X }+ A_{Y}**

**A = A’ + A _{Z}**

When **A** is directed within an octant of the parallelogram law, we may resolve the vector into components **A = A’ + A _{Z}** and then A’ = AX + AY

#### Cartesian Unit Vector for Force Vector (3D)

In 3D, the set of Cartesian unit vector i, j, k is used to designate the direction of the axis.

**A = A _{X }i + A_{Y} j + A_{Z}k**

#### Coordinate Direction Angle

**Cosα = A _{x}/A**

**Cosβ = A _{y}/A**

**Cosγ = A _{z}/A**

These are known as the direction cosines of A. Once they have been obtained, the coordinate direction angle **α, ****β** and**γ **can then be determined from the inverse cosines.

An easy way of obtaining these directions Cosines is to form a unit vector **u** in the direction of A. If **A** is expressed in cartesian vector form **A = A _{X }i + A_{Y} j + A_{Z}k **then

**u**will have a magnitude of one and it will be dimensionless.

u = A_{x}/A(**i**) + A_{y}/A(**j**) + A_{z}/A(**k**)

#### Transverse and Azmuth Angles

The direction of **A** can be specified using two angles, namely a transverse angle ϑ and an azmuth angle.

you may visit the previous lecture for a better understanding of the topic.