WHAT IS THE VECTOR QUANTITY? (WITH EXAMPLES) - MATHS - 2024

The vector quantity, or vector, is defined as that for which it is necessary to specify both its magnitude or module (with the respective units) and its direction.

Unlike the vector quantity, a scalar quantity has only magnitude (and units), but no direction. Some examples of scalar quantities are temperature, volume of an object, length, mass, and time, among others.

Difference between vector quantity and scalar

In the following example you can learn to differentiate a scalar quantity from a vector quantity:

A speed of 10 km / h is a scalar quantity, while a speed of 10 km / h to the north is a vector quantity. The difference is that in the second case a direction is specified, in addition to the magnitude.

Vector quantities have a myriad of applications, especially in the world of physics.

Graphs and Denotations of a Vector Quantity

The way to denote a vector quantity is by placing an arrow (→) on the letter to be used, or by writing the letter in bold (a).

To graph a vector quantity you need a reference system. In this case, the Cartesian plane will be used as the reference system.

The graph of a vector is a line whose length represents the magnitude; and the angle between said line and the X axis, measured counterclockwise, represents its direction.

You must specify which is the starting point of the vector and which is the arrival point. An arrow is also placed at the end of the line that points to the arrival point, which indicates the direction of the vector.

Once a reference system has been set, the vector can be written as an ordered pair: the first coordinate represents its magnitude and the second coordinate its direction.

Examples

1- Gravity acting on an object

If an object is placed at a height of 2 meters above the ground and it is released, gravity acts on it with a magnitude of 9.8 m / s², and a direction perpendicular to the ground in a downward direction.

2- Movement of an airplane

An airplane that traveled from point A = (2,3) to point B = (5,6) of the Cartesian plane, with a speed of 650 km / h (magnitude). The direction of the trajectory is 45º northeast (direction).

It should be noted that, if the order of the points is reversed, then the vector has the same magnitude and the same direction, but a different sense, which will be southwest.

3- Force applied to an object

Juan decides to push a chair with a force of 10 pounds, in a direction parallel to the ground. The possible directions of the applied force are: to the left or to the right (in the case of the Cartesian plane).

As in the previous example, the sense that John decides to give the force will produce a different result.

This tells us that two vectors can have the same magnitude and direction, but be different (they produce different results).

Two or more vectors can be added and subtracted, for which there are very useful results, such as the Law of Parallelogram. You can also multiply a vector by a scalar.

References

1. Barragan, A., Cerpa, G., Rodríguez, M., & Núñez, H. (2006). Physics For High School Cinematics. Pearson Education.
2. Ford, KW (2016). Basic Physics: Solutions to the Exercises. World Scientific Publishing Company.
3. Giancoli, DC (2006). Physics: Principles with Applications. Pearson Education.
4. Gómez, AL, & Trejo, HN (2006). Physics l, A constructivist approach. Pearson Education.
5. Serway, RA, & Faughn, JS (2001). Physical. Pearson Education.
6. Stroud, KA, & Booth, DJ (2005). Vector Analysis (Illustrated ed.). Industrial Press Inc.
7. Wilson, JD, & Buffa, AJ (2003). Physical. Pearson Education.