Scalar vs. vector
In mathematics and physics, scalar and vector quantities are pivotal in understanding physical phenomena. These two quantities are fundamental building blocks that help us understand objects around us.
In this Answer, we will be making a comparison between these two quantities to understand the significant differences between them. Let's start with their definitions.
Scalar: A quantity that has a
Vector: A quantity that has a magnitude and a direction. Examples of vectors include force, and displacement
Comparison
The diagram below illustrates the difference between a vector and a scalar using an example.
The diagram compares a scalar quantity (speed) and a vector quantity (velocity). Speed tells about the magnitude of a motion without the direction associated with it, while velocity tells the magnitude of an object's motion and includes the direction of that motion.
Let's look at more differences between these two quantities in the table below.
Scalar vs. vector
Scalar | Vector | |
Direction | It gives information on the magnitude only without the direction. | It gives information on the magnitude and the direction. |
Dimension | It has no direction, so it has only one dimension. | It has a direction, so it has multiple dimensions. |
Division operation | Division of two scalars is possible. | Division of two vectors is not possible. |
Change | It can change by changing the magnitude value. | It can change by changing the magnitude value or direction or both. |
Algebraic operations | Normal algebraic operations are applied to it. | Special vector algebraic operations are applied to it. |
Representation | It is represented by a numerical value. | It is represented by an alphabetic letter with an arrowhead on top of it. |
Resolution into components | It can not be resolved into its components. | It can be resolved into its components using sin and cos operations. |
Operations result | Operations on two scalars always result into a scalar. | Operations on two vectors result into a scalar or vector. |
Examples | Its examples include speed and distance. | Its examples include velocity and displacement. |
Conclusion
Scalars and vectors are important quantities in physics and mathematics that help us represent directionless and directional quantities, respectively. Understanding their differences helps us understand their distinct behaviors and applications in various areas of science. For instance, scalars are useful in measuring distances and numeric quantities, while vectors play vital roles in navigation systems and computer graphics.
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