About This Chapter
Scalars & Vectors in Algebra - Chapter Summary
In this chapter, our instructors will define scalars and vectors and explain the importance of knowing the difference. You will learn to add, subtract, multiply and divide vectors as well as how to work with vectors in two and three dimensions. How to graph vectors and use vector diagrams is also covered.
Your study will continue with an explanation of dot products and cross products, as well as vector resolution and work as it relates to variable force. This chapter will show you how to do the following:
- Differentiate between vectors and scalars
- Add, subtract, multiply and divide vectors
- Work with vectors in two and three dimensions
- Use vector diagrams
- Tell the difference between a dot product and a cross product
- Solve problems using vector resolution
- Understand and calculate variable forces
Our mobile-friendly study materials are accessible 24 hours a day, seven days a week. Use the quizzes and chapter tests to measure how well you understand the subject and where you may need additional review. If you have questions as you work through the lessons, contact one of our instructors for more help.
1. 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.
2. Vectors: Definition, Types & Examples
In this lesson, learn what vectors are and how to represent them mathematically. You will also learn how to tell if two vectors are equal, parallel, collinear, or coplanar.
3. 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.
4. Vectors in Two & Three Dimensions
Two-dimensional and three-dimensional vectors are very similar, and operations that can be performed on two-dimensional vectors can also be performed in similar ways on three-dimensional vectors. In this lesson, learn about both types of vectors.
5. 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.
6. What are Vector Diagrams? - Definition and Uses
After watching this video, you will be able to explain what vector diagrams are and how they are used, including vector addition and subtraction. A short quiz will follow.
7. The Dot Product and Vectors: Definition & Formula
After watching this lesson, you will be able to explain what a dot product is, how it is different from a cross product, and use equations to calculate dot products. A short quiz will follow.
8. 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.
9. Vector Resolution: Definition & Practice Problems
After watching this lesson, you will be able to explain what vector resolution is and solve problems involving vector resolution. A short quiz will follow.
10. Work Done by a Variable Force
Doing work on an object is a simple concept: we apply a certain force over a certain distance. But in real life, that force is rarely constant. Therefore, we need to understand variable forces and be able to calculate them accurately.
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Other chapters within the NDA Exam Preparation & Study Guide course
- About the NDA Exam
- Algebra Concepts
- Advanced Algebra Concepts
- Solving Matrices & Determinants
- Trigonometry Concepts
- Geometry & Linear Equations
- Analytic Geometry
- Functions, Limits & Continuity
- Derivative Rules
- Calculations & Applications of Derivatives
- Integral Calculus
- Differential Equations & Applications
- Visualizing Statistics
- Probability Concepts in Math
- Grammar and Usage
- Improving Reading Comprehension
- Measurements in Physics
- Motion in Physics
- Basics of Work, Power & Energy
- Understanding Heat Transfer
- Sound Waves
- Light, Mirrors & Lenses
- Electric Currents & Power
- Scientific Technology, Machines & Tools
- The Atom & Structure of Elements
- Chemical Properties of Elements & Substances
- Chemical Symbols, Formulas & Reactions
- Qualities of Living Organisms
- Health Science Basics
- Solar System & Eclipses
- Achievements of Famous Scientists
- Indian History
- Overview of Major World History Events
- World Government Types
- The Earth
- Earth's Oceans, Atmosphere & Climate
- Regional Geography of South Asia
- Modern Day Events in India
- NDA Exam Preparation & Study Guide Flashcards