Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
In addition to the revision notes for Vectors and Scalars on this page, you can also access the following Vectors and Scalars learning resources for Vectors and Scalars
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 2.1 | Vectors and Scalars |
In these revision notes for Vectors and Scalars, we cover the following key points:
A vector (in mathematics) is a quantity that has both a magnitude (numerical value or size) and a direction. If one of them is missing, the information is incomplete.
Geometrically, a vector is represented through an arrow. The tip shows the direction and the ending point while the toe shows the starting point of the vector.
On the other hand, a quantity which has only magnitude (does not involve direction), is known as "scalar". For example, real numbers are scalars. You simply need to know their numerical value to have a complete information regarding the quantity involved.
All quantities in Physics are either vector or scalar. For example, Force is a vector quantity as it involves direction, while Temperature is a scalar because only its numerical value is required. However, in Physics, vectors and scalars are different from those discussed in Maths. The table below sheds light at this point.
| Property | Scalars in Maths | Vectors in Maths | Scalars in Physics | Vectors in Physics |
|---|---|---|---|---|
| Magnitude | ✓ | ✓ | ✓ | ✓ |
| Direction | × | ✓ | × | ✓ |
| Unit | × | × | ✓ | ✓ |
| Application point | × | × | × | ✓ |
Not all vectors lie according the known basic directions. Hence, it is better to split them into components to ease their study. In this way, any vector AB⃗ splits into two components: the horizontal (x - component) and the vertical (y - component).
Magnitude of a vector AB represents its length in the given units. We can use the Pythagorean Theorem to calculate it. Thus,
To find the angle formed by a vector with a certain direction, we use the following trigonometric formulae:
where Θ is the angle formed by the adjacent side and hypotenuse.
Enjoy the "Vectors and Scalars" revision notes? People who liked the "Vectors and Scalars" revision notes found the following resources useful:
Please provide a rating, it takes seconds and helps us to keep this resource free for all to use
We hope you found this Physics tutorial "Vectors and Scalars" useful. If you did it would be great if you could spare the time to rate this physics tutorial (simply click on the number of stars that match your assessment of this physics learning aide) and/or share on social media, this helps us identify popular tutorials and calculators and expand our free learning resources to support our users around the world have free access to expand their knowledge of physics and other disciplines.