About This Chapter
Vectors & Scalars in Math - Chapter Summary
In this chapter, our instructors present you with vectors in physics and demonstrate how they can be manipulated in math. These interesting lessons explain the difference between scalars and vectors and show you how to use geometry to add vectors. You'll review basic calculations involving scalar multiplication and understand how to find the cross product of two vectors. Other topics include the triple scalar product, which occurs when you multiply three vectors together. This informative chapter prepares you to do the following:
- Graph vectors with regard to direction and magnitude
- Add, subtract, multiply and divide vectors
- Find the dot product of vectors using algebra and geometry
- Calculate the direction of a vector when given the x and y components
For a flexible, mobile-friendly study resource, check out our video and text lessons. Created to teach you the essential topics in an easy-to-follow way, our learning materials are accessible to you on any mobile device at any time. Our instructors can offer their assistance if you struggle while working through the chapter. Use the printable transcripts to create portable study guides that focus on the most important topics included in the lesson.
1. What Is a Vector? - Definition & Types
After watching this lesson, you will be able to explain what vectors are in physics, give some examples of vectors and have a basic idea of how they can be manipulated mathematically. A short quiz will follow.
2. Scalars and Vectors: Definition and Difference
In this lesson, we will examine scalars and vectors, learn why it is important to know the difference between the two and why remembering to add a direction to many of your exam answers could be the reason you get it right or wrong.
3. Graphing Vectors in Math: Magnitude & Direction
Vectors are some of the most useful parts of math, but their usefulness is only apparent if you know how to graph them. In this lesson, we learn how to graph vectors with respect to both magnitude and direction.
4. Vectors in Math: Addition, Subtraction, Division & Multiplication
From airplanes to walking in a straight line, vectors are everywhere. In this lesson, we're going to learn how to add, subtract, multiply, and divide vectors helping us make more sense of them.
5. Vector Addition (Geometric Approach): Explanation & Examples
After watching this video, you will be able to explain why we might need to add two vectors and, given magnitudes and directions, add two vectors using geometric methods. A short quiz will follow.
6. Scalar Multiplication of Vectors: Definition & Calculations
After watching this video, you will be able to explain what scalar multiplication is and complete basic calculations involving the scalar multiplication of vectors. A short quiz will follow.
7. Performing Operations on Vectors in the Plane
After watching this video lesson, you should be able to add, subtract, and multiply your vectors. Learn how easy it is to perform these operations and what you need to keep in mind when performing these operations.
8. The Dot Product of Vectors: Definition & Application
After watching this video lesson, you will be able to find the dot product of vectors both algebraically and geometrically. Learn the difference between the two and what you need in order to calculate them.
9. Finding The Cross Product of Two Vectors
After watching this lesson, you will be able to explain what a cross product is and calculate the cross product of two vectors. A short quiz will follow.
10. Vector Components: The Direction of a Vector
After watching this lesson, you will be able to explain what is meant by the direction of a vector and calculate the direction of a vector when given the x and y components. A short quiz will follow.
11. Triple Scalar Product: Definition, Formula & Example
Vectors and scalars are often discussed in physics. In this lesson, we define a particular multiplication of three vectors called the triple scalar product and use an example to show how it is calculated.
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Other chapters within the BITSAT Exam - Math: Study Guide & Test Prep course
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- Complex Numbers & Polynomials in Algebra
- Introduction to Quadratics
- Working with Quadratic Functions Overview
- Mathematical Sequences & Series Overview
- Series & Sequences Application
- Exponential Functions & Logarithmic Equations
- Binomial Theorem Overview
- Overview of Matrices & Determinants
- Sets & Relations in Math
- Introduction to Trigonometric Functions
- Trigonometric Identities Overview
- Real World Trigonometric Applications
- Operating with Functions
- Solving Inequalities
- Two-Dimensional Coordinate Geometry
- Straight Lines & Angles in Coordinate Geometry
- Circular Arc & Circles in Coordinate Geometry
- Conic Sections in Coordinate Geometry
- Three-Dimensional Coordinate Geometry
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- Calculating Derivatives
- Differentiable Functions & Min-Max Problems
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- Dispersion & Frequency Distributions in Statistics
- Linear Programming & Systems of Equations
- Definite Integrals
- Permutation & Combination
- Mathematical Modeling Overview
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