9 julio, 2024

Vector quantities: what they are and examples

What are vector quantities?

It defines the vector quantityor vector, as the one for which it is necessary to specify both its magnitude or module (with the respective units) and its direction.

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

Difference Between Vector and Scalar Quantity

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 due 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 an infinite number 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 (→) over the letter to be used, or writing the letter in bold (to).

To graph a vector quantity, a reference system is needed. 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 is fixed, the vector can be written as an ordered pair: the first coordinate represents its magnitude and the second coordinate its direction.

Examples of vector quantities

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) on the Cartesian plane, with a speed of 650 km/h (magnitude). The direction of the trajectory is 45° 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 direction, which will be to the 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 meaning that Juan decides to give to force will produce a different result.

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

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

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