## Test (Brandon)

Scalars and vectors are mathematical objects that are used to quantify physical quantities.

### Interactive Example Link Out

Nulla vitae elit libero, a pharetra augue. Cras mattis consectetur purus sit amet fermentum. Maecenas sed diam eget risus varius blandit sit amet non magna.

**Scalar.** A scalar is a real number. For example , , , , and so on .

### EXAMPLE asdfasfd

Vestibulum id ligula porta felis euismod semper. Maecenas sed diam eget risus varius blandit sit amet non magna.

Vestibulum id ligula porta felis euismod semper. Maecenas sed diam eget risus varius blandit sit amet non magna.

### EXAMPLE Heading 1

Vestibulum id ligula porta felis euismod semper. Maecenas sed diam eget risus varius blandit sit amet non magna.

**Scalar quantity.** A scalar quantity is a quantity that can be described by a single real number. This number specifies the magnitude or size of that quantity. For example length, angle, mass, speed, area, temperature, and pressure are scalar quantities.

### Interactive Example Link Out

Nulla vitae elit libero, a pharetra augue. Cras mattis consectetur purus sit amet fermentum. Maecenas sed diam eget risus varius blandit sit amet non magna.

Sometimes a scalar quantity is simply referred to as scalar. For example, “mass is a scalar” is equivalent to stating: “mass is a scalar quantity”.

The mathematical operations on scalars follow the usual rules of arithmetic.

### EXAMPLE Heading 2

**Vector.** A vector is a mathematical object that has a size (magnitude) and a direction. This definition perfectly fulfills the requirements of engineering mechanics. However, for a more rigorous mathematical definition, please refer to section 2.8.

**Vector quantity.** A vector quantity is a quantity characterized by both a magnitude and a direction. For example velocity, force, acceleration, and moment are all vector quantities.

#### EXAMPLE Heading 3

Curabitur blandit tempus porttitor. Integer posuere erat a ante venenatis dapibus posuere velit aliquet. Nullam id dolor id nibh ultricies vehicula ut id elit.

The **magnitude** (sometimes referred to as the norm) of a vector is a positive scalar. For example the magnitude of the velocity of a moving object is the speed of that object. Speed is always measured and reported as a positive number. The magnitude of a physical quantity must have a unit.

The line that is collinear with an arrow is called the **line of action**. The **orientation** or direction of an arrow (its tail is already known or defined) with respect to a fixed axis is defined by an angle formed between the axis and the line of action of the arrow. Fig. 2.2 shows a directed line segment or arrow representing the vector with its defined terms.

**Zero vector.** The zero vector, denoted by or , is a vector of length zero. The zero vector does not point toward any direction, therefore, its direction is undefined.

It should be noted that a vector (directed line segment) is defined by only two parameters being magnitude and direction. Therefore, the position of a vector in the space does not change the properties. As a result, two vectors are equal if they have the same direction and magnitude. Examples of equal vectors are shown in Fig. 2.3a.

**Parallel vectors.** Two vectors are parallel if they have parallel lines of action. In other words, two parallel vectors have the same or opposite sense of directions. Examples of parallel vectors are shown in Fig. 2.3.b.

This geometric representation applies to vectors in a plane (a two-dimensional space) or in a three-dimensional space.