> [!summary] Scalars have magnitude > Vectors have magnitude and direction >[!info]+ Read Time **⏱ 1 min** # Definition A scalar is something that does not have direction. It is just a measurement (has magnitude). For example, [[Energy|energy]] is a scalar because it is just a measurement. A vector is something that has direction. It is also a measurement (has a magnitude) but also direction. For example, applying a [[Forces|force]] on an object depends on how much you are pushing it (measurement) and the direction where you are pushing it (direction) ## Mathematical Rules To mathematically get vectors and scalars, this is a general rule for addition, multiplication and [[Dots Product & Angles|dot products]]. | Form | Type | Outcome | | ------------- | --------------------- | ----------- | | Multipication | Scalar x Vector | Vector | | Mutipication | Scalar x Scalar | Scalar | | Additon | Vector + Vector | Vector | | Additon | Vector + Scalar | Not allowed | | Dot Product | Scalar $\cdot$ Vector | Vector | | Dot Product | Scalar $\cdot$ Scalar | Scalar | | Norm | Vector | Scalar | | Norm | Scalar | Scalar | > [!note] Addition of a vector and scalar is not allowed because they are fundamentally different quantity. # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/iLB_4Wu2QOg?si=YLceb1wWUFvfJwFk" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- > 🧠 Enjoy this walkthrough? [Support Math & Matter](https://github.com/rajeevphysics/Obsidian-MathMatter) with a star and help others learn more easily. ---