V - Vectors Module Overview

Vectors Module Overview

Introduction

In this module, we will learn about vectors! You may have heard of them before in Physics, but the big idea will be to understand how two forces work on object. You will utilize right triangle trigonometry as well as Unit Circle trigonometry.

Essential Questions

How are vector and scalar quantities similar and different?
How can I use vector operations to model, solve and interpret real-world problems?
How can I represent addition, subtraction, and scalar multiplication geometrically?
What are different ways to geometrically represent the addition of vectors?
In what ways can matrices transform vectors?

Vectors Key Terms

The following key terms will help you understand the content in this module.

Vector – A mathematical object that has both magnitude and direction, expressed as v, equation image indicator $LaTeX: \overline{v}$ $\overline{v}$ , or〈a,b〉or as a directed line segment.

Scalar – A real number. A scalar has a magnitude but not direction.

Initial Point – The point at the tail of the arrow representing a vector. The initial point is the origin if the vector is in standard position.

Terminal Point – The point at the "tip" of the arrow representing a vector.

Magnitude of a Vector – The distance between vector's initial and terminal points denoted ‖v‖, | equation image indicator $LaTeX: \overline{v}$ $\overline{v}$ |, or |v|. $LaTeX: \lVert{v}\rVert = \lVert{a, b}\rVert =\sqrt{a^2 +b^2}$ $\lVert{v}\rVert = \lVert{a, b}\rVert =\sqrt{a^2 +b^2}$ .

Components of a Vector – a and b in the vector〈a,b〉. The horizontal component is a and the vertical component is b.

Parallel Vectors – Two or more vectors whose directions are the same or opposite.

Equivalent Vectors – Two or more vectors that have the same direction and magnitude.

Resultant Vector – The vector that results from adding two or more vectors.

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