Physics Tutorial 2.3 - Multiplication of a Vector by a Scalar

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There are 4 lessons in this physics tutorial covering Multiplication of a Vector by a Scalar. The tutorial starts with an introduction to Multiplication of a Vector by a Scalar and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific physics lesson as required to build your physics knowledge of Multiplication of a Vector by a Scalar. you can access all the lessons from this tutorial below.

In addition to the tutorial for Multiplication of a Vector by a Scalar on this page, you can also access the following Vectors and Scalars learning resources for Multiplication of a Vector by a Scalar

In this Physics tutorial, you will learn:

The meaning of "Multiplication of a vector by a scalar"
How to express the division of a vector by a scalar in terms of multiplication?
What are some examples involving the multiplication of a vector by a scalar in Physics?
How to multiply a vector by a scalar in coordinates?

Introduction

In geometry, precisely when discussing about similar figures, you have learned that two similar figures are identical in shape but their dimensions are different. For example, two squares are similar as they have the same features; they both have 4 equal sides, 4 right angles, 2 equal diagonals, etc. However, their respective sides' length are different. Look at the figure:

From the similarity rules, we can write for the above squares:

Square 2 = 2 × Square 1

As the sides of the second square are twice the length of those in the first square (6cm = 2 × 3cm). (Do not confuse the magnitudes of the respective surface areas with the sides' dimension. The area of the second square is 4 times the area of the first square, but here we simply wrote "Square 2 = 2 × Square 1", not "Area of Square 2 = 2 × Area of Square 1").

It is clear that both figures have the same features except their dimensions. For instance, their lower base is horizontal; the lateral sides are vertical in both squares and so on. Hence, we can say, "In similar figures, all the other features except the dimensions are the same". This affirmation will help you in understanding the multiplication of a vector by a scalar.

Please select a specific "Multiplication of a Vector by a Scalar" lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this physics topic.

Vectors and Scalars Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
2.3	Multiplication of a Vector by a Scalar
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
2.3.1	Multiplying a vector by a positive scalar
2.3.2	Division of a vector by a scalar as multiplication with the inverse
2.3.3	Multiplying a vector by a negative scalar
2.3.4	How to multiply a vector by a scalar in coordinates?

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Physics Tutorial 2.3 - Multiplication of a Vector by a Scalar

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