Non-Coplanar Force System

Here are some useful and helpful lectures I found for Non-Coplanar Force System:

Introduction to Non-Coplanar Force System
Applied Mechanics By Hervey F. Girvin

Vector Multiplication: Cross Product

We define the cross product of two three-dimensional vectors a and b by the requirements:

• a × b is a vector that is perpendicular to both a and b.
• ||a × b|| is the area of the parallelogram spanned by a and b (i.e. the parallelogram whose adjacent sides are the vectors a and b).
• The direction of a×b is determined by the right-hand rule. (This means that if we curl the fingers of the right hand from a to b, then the thumb points in the direction of a × b.)

Vector Multiplication: Dot Product

The multiplication of two vectors, is not uniquely defined, in the sense that there is a question as to whether the product will be a vector or not. For this reason there are two types of vector multiplication.
First, the scalar or dot product of two vectors, which results in a scalar.
And secondly, the vector or cross product of two vectors, which results in a vector.

In this tutorial we shall discuss only the scalar or dot product.