2: Forces and Other Vectors
- Page ID
- 70206
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Before you can solve statics problems, you will need to understand the basic physical quantities used in Statics: scalars and vectors.
- Scalars are physical quantities which have no associated direction and can be described by a positive or negative number, or even zero. Scalar quantities follow the usual laws of algebra, and most scalar quantities have units. Mass, time, temperature, and length are all scalars.
- Vectors represent physical quantities which have magnitude and a direction. Vectors are identified by a symbolic name which will be typeset in bold like \(\vec{r}\) or \(\vec{F}\) to indicate its vector nature. The primary vector quantity you will encounter in statics will be force, but moment and position are also important vectors. Computations involving vectors must always consider the directionality of each term and follow the rules of vector algebra as described in this chapter.
- 2.7: Dot Products
- Unlike ordinary algebra where there is only one way to multiply numbers, there are two distinct vector multiplication operations. The first is called the dot product or scalar product because the result is a scalar value, and the second is called the cross product or vector product and has a vector result. The dot product will be discussed in this section and the cross product in the next.