Physics

Dynamics

# Vectors and Scalars

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Vectors and Scalars

Vectors and Scalars Overview

**Vectors**and**scalars**are both types of quantities in physics that are expressed as measurements.- A
**scalar**quantity is only defined by its magnitude. - A
**vector**quantity is defined by both its magnitude and its direction. - Examples of scalar quantities include speed, distance, mass, temperature and energy.
- Examples of vector quantities include displacement, velocity, force and acceleration.

Scalars

- A
**scalar**has only magnitude (size). - Scalars can be added, subtracted, multiplied, and divided like normal numbers, which is termed as scalar arithmetic.
- Examples of scalar quantities:
**Mass**,**distance**,**speed**,**time**,**temperature**and**energy**. - Note that speed is a scalar. It measures the rate of change of distance but disregards the direction of motion.

Vectors

**Vectors**have both magnitude and a direction.- The
**direction**component of a vector separates it from a scalar quantity. - Vectors are represented by arrows, where the arrowhead points to the direction and the length signifies the magnitude.
- Vector quantities include:
**Displacement**,**velocity**,**acceleration**, and**force**. - Displacement, velocity, and acceleration are vectors associated with motion.
- It's important to distinguish between velocity (a vector) and speed (a scalar). Velocity includes the speed of an object and its direction of motion.
- Vectors can be added or subtracted — this is a process called vector addition or vector resolution.

Vector Addition

**Vector addition**involves geometrical methods to 'add' vectors known as the "head-to-tail" method or parallelogram method.- If multiple vector quantities are affecting a single body, the
**resultant vector**can be found using vector addition methods. - Negative vectors: A vector in the opposite direction is considered ‘negative’.

Scalar and Vector Products

- The
**dot product**or scalar product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number. - The
**cross product**, also known as vector product, outputs a vector which is perpendicular to the vectors being multiplied. The asocioated rules are as per the right-hand rule.

In both the scalar and vector products, consideration must be given to the units used in order to maintain consistency and accuracy.