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phys: add more introductory information on vectors

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eggy 2020-09-22 09:35:06 -04:00
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@ -150,14 +150,25 @@ $$intercept_{best fit} ± intercept_{max} - intercept_{min}$$
## 1.3 - Vectors and scalars
!!! note "Definition"
- **Scalar:** A physical quantity with a numerical value and unit.
- **Vector:** A physical quantity with a numerical value, unit, and **direction.**
- **Scalar:** A physical quantity with a numerical value (magnitude) and a unit.
- **Vector:** A physical quantity with a numerical value (magnitude), a unit, and a **direction.**
??? example
- Physical quantities represented by scalars include speed, distance, mass, temperature, pressure, time, frequency, current, voltage, and more.
- Physical quantities represented by vectors include velocity, displacement, acceleration, force (e.g., weight), momentum, impulse, and more.
- Scalar quantities include speed, distance, mass, temperature, pressure, time, frequency, current, voltage, and more.
- Vector quantities include velocity, displacement, acceleration, force (e.g., weight), momentum, impulse, and more.
Vectors are represented as arrows whose length represents their scale/magnitude and their orientation refer to their direction.
Vectors are drawn as arrows whose length represents their scale/magnitude and their orientation refer to their direction.
!!! info
- A variable representing a vector is written with a right-pointing arrow above it.
- The **standard form** of a vector is expressed as its magnitude followed by its unit followed by its direction in square brackets.
$$\vec{a} = 1\text{ m }[N 45° E]$$
- The **component form** of a vector is expressed as the location of its head on a cartesian plane if its tail were at $(0, 0)$.
$$\vec{a} = (1, 1)$$
!!! example
The below shows a vector with a magnitude of 1, unit of metre, pointing north.
$$\vec{a} = 1\text{ m }[N]$$
### Adding/subtracting vectors diagrammatically