What is Scalars and Vectors? | Definition, Types, Formula & Examples

What is Scalars and Vectors?

There are many different mathematical quantities used in physics. Examples of these include acceleration, velocity, velocity, force, work, and power. These different quantities are often described as “scalar” or “vector” quantities. Below, we will discuss the meanings of these words and introduce some basic vector math.

What is a Scalar?

A scalar is a quantity that is fully described only by magnitude. It is described by a single number. Some examples of scalar quantities consist of speed, volume, mass, temperature, power, energy, and time.

What is a Vector?

A vector is a quantity that has both a magnitude and a direction. Vector quantities are important in the study of motion. Some examples of vector quantities consist of force, velocity, acceleration, displacement, and momentum.

What is the difference between a Scalar and Vector?

A vector quantity has direction and magnitude, while a scalar quantity has only one magnitude. You can tell whether a quantity is a vector based on whether it has a direction associated with it.

Example:

Velocity is a scalar quantity, but velocity is a vector that defines both direction and magnitude. Velocity is the magnitude of velocity. A car traveling at 40 mph is going east. It has a speed of 40 miles per hour.

How to Draw a Vector

A vector is drawn as an arrow with a head and a tail. The magnitude of the vector is usually described by the length of the arrow. Arrows point in the direction of the vector.

How to Write a Vector

Vectors are usually bold. They can also be written with an arrow above the letter.

Example questions: Is it a scalar or a vector?

1) The soccer player is running 10 miles per hour toward the end of the field.

It’s a vector because it represents magnitude (10 mph) and direction (towards the end zone). This vector represents the speed of the soccer player.

2) The volume of this box on the west side of the building is 14 cubic feet.

This is a scalar. This can be a bit complicated since it indicates the location of the box on the west side of the building, but it has nothing to do with the direction of the 14-cubic-foot block.

3) The temperature in the room is 15 degrees Celsius.

It is scalar, has no direction.

4) The car accelerates north at 4 meters per second squared.

It is a vector because it has both direction and magnitude. We also know that acceleration is a vector quantity.

Interesting Facts about Scalars and Vectors

Unit vectors are vectors of magnitude 1. They are used to specify direction. Credit for the invention of vectors usually goes to the Irish physicist William Rowan Hamilton.

Vectors and scalars are important in many areas of math and science.

Vectors can be defined in two- or three-dimensional space.

Vector graphics are sometimes used in computers because they can be scaled to a larger size without loss of image quality.