Do you know how to represent a quantity with a direction? Can we represent 5 km to North in one single entity? Yes, we can with the help of vectors. In the section, we will learn about the Vector Algebra which will consist of the basic concepts, components, types and operations on the vectors. Let’s study the topic below.
- Basic Concepts of Vectors
- Components of a Vector
- Types of Vectors
- Addition of Vectors
- Scalar (or Dot) Product of Two Vectors
- Vector (or Cross) Product of Two Vectors
- Section Formula
- Projection of a Vector on a Line
Q1. What is a Vector in Math?
A1. We can define a vector as an object that has both a direction and a magnitude. Geometrically, we can represent a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. Moreover, two examples of vectors are those that characterize force and velocity.
Q2. How do vectors work?
A2. Vectors refers to lines that represent both direction and magnitude (size). Consequently, if an object move in more than one direction or more than one force acts upon an object equivalently, then we can add the vectors to find a resultant displacement or resultant force that acts on it.
Q3. What does ‖ A ‖ mean?
A3. “‖” means that the lines are parallel to each other. In a square, all the opposite sides are parallel which means that they never intersect each other at any point and are parallel to infinity. The most practical example of parallel lines is railway tracks that never join each other.
Q4. Is position a vector?
A4. Yes, the position is a vector quantity. Because it has a magnitude (size) as well as a direction. Moreover, the magnitude of a vector quantity is a number (with units) that tells how much of the quantity there is and the direction tells you which way the vector is pointing.