Vectors
Vectors (or Vector Quantities) are the combination of two scalars. (Two units, each only with a magnitude only.) Direction and Distance are two common scalars, that combine to form Direction, a vector.
In order to describe any type of motion in the real world, we are using distance in a new way, in conjunction with direction. A distance has very little value in practical application without a direction attached to it. If I give you the distance to the town on a signpost in the middle of knowhere.
From whatever place in the world you live in, if I were to tell you to go to a specific place 50 km away from you, that information is utterly useless because it could be anywhere 50 kilometers away.
(Literally a 50km radius away from your current position.)
When we attach direction to distance, we get a very specific quantity called a vector, which in this case is called displacement — motion.
What Is A Vector
“Vector products of vectors define still other fundamental vector physical quantities, such as torque and angular momentum. In other words, vectors are a component part of physics in much the same way as sentences are a component part of literature.” [1]
Vectors Contents
- Scalars and Vectors
- Components of a Vector
- Coordinate Systems
- Algebra of Vectors
- Products of Vectors
—– Notes —–
Notes
Openstax. University Physics Volume 1. Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction
[Image Caption] Figure 2.1 A signpost gives information about distances and directions to towns or to other locations relative to the location of the signpost. Distance is a scalar quantity. Knowing the distance alone is not enough to get to the town; we must also know the direction from the signpost to the town. The direction, together with the distance, is a vector quantity commonly called the displacement vector. A signpost, therefore, gives information about displacement vectors from the signpost to towns. (credit: modification of work by “studio tdes”/Flickr, thedailyenglishshow.com)
Chapter Outline
2.2 Coordinate Systems and Components of a Vector
Introduction
Vectors are essential to physics and engineering. Many fundamental physical quantities are vectors, including displacement, velocity, force, and electric and magnetic vector fields. Scalar products of vectors define other fundamental scalar physical quantities, such as energy. Vector products of vectors define still other fundamental vector physical quantities, such as torque and angular momentum. In other words, vectors are a component part of physics in much the same way as sentences are a component part of literature.
In introductory physics, vectors are Euclidean quantities that have geometric representations as arrows in one dimension (in a line), in two dimensions (in a plane), or in three dimensions (in space). They can be added, subtracted, or multiplied. In this chapter, we explore elements of vector algebra for applications in mechanics and in electricity and magnetism. Vector operations also have numerous generalizations in other branches of physics.
Resources
- William Moebs, Samuel J. Ling, Jeff Sanny. University Physics Volume 1. OpenStax. Sep 19, 2016. Houston, Texas. Book URL:<https://openstax.org/books/university-physics-volume-1/pages/1-introduction>.
Section URL: <https://openstax.org/books/university-physics-volume-1/pages/2-introduction>.