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What's a Column Vector? Easy Math Fun

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What's a Column Vector? Easy Math Fun
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Philippa Williams

@philippailliams_jwxn

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3 Followers

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The column vector mathematical concept explains vectors as quantities with magnitude and direction, represented through arrows and numerical components, forming a fundamental basis for mathematical calculations and spatial understanding.

  • Vectors are represented using column format with two numbers indicating horizontal and vertical movements
  • The vector scalar multiplication explanation shows how normal numbers (scalars) can modify vector components
  • The add column vectors method involves combining corresponding components of different vectors
  • Different notations exist for vectors including bold letters, underlined symbols, and arrow representations
  • Negative vectors maintain the same magnitude but move in opposite directions

09/09/2023

276

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

View

Page 2: Vector Representations and Scalar Operations

This page covers various ways to represent vectors and introduces scalar multiplication. It explains how vectors can be written using different notations and how they interact with scalar values.

Vocabulary: Scalar - a regular number used to multiply vector components.

Example: When multiplying vector a=(2,4) by 2, the result is 2a=(4,8).

Highlight: A negative vector (-a) maintains the same magnitude as the original vector (a) but points in the opposite direction.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

View

Page 3: Vector Addition and Calculations

This page focuses on the process of adding column vectors and performing more complex vector calculations. The content demonstrates how to combine vectors through component-wise addition.

Definition: Vector addition involves adding corresponding components of two or more vectors.

Example: For vectors a=(3,5) and b=(2,11), their sum a+b=(5,16).

Highlight: Complex vector expressions can involve multiple operations including addition, subtraction, and scalar multiplication.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

View

Page 4: Vector Fundamentals Review

This page revisits the basic concepts of vectors, reinforcing the understanding of magnitude and direction. It provides additional examples of vector representation and movement.

Definition: Vectors represent quantities with both size (magnitude) and direction.

Example: Drawing vectors as arrows helps visualize their direction and magnitude.

Highlight: The column vector notation provides a precise way to specify both horizontal and vertical movements.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

View

Page 5: Advanced Vector Operations

This page delves into more sophisticated vector operations and representations, expanding on scalar multiplication and directional concepts.

Example: Vector AB=(-3) represents movement from point A to point B.

Highlight: The direction of vector arrows is crucial for understanding the movement from one point to another.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

View

Page 6: Complex Vector Calculations

This page concludes with advanced vector calculations, demonstrating how to perform multiple operations with vectors simultaneously.

Example: The calculation 2a-3b combines scalar multiplication and vector addition.

Highlight: Complex vector expressions can be solved by breaking them down into individual operations and following the order of operations.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

View

Page 1: Introduction to Vectors and Column Vectors

This page introduces the fundamental concepts of vectors and their representation in column format. The content explains how vectors possess both magnitude and direction, visualized through arrows.

Definition: A vector is a quantity defined by both magnitude (size) and direction.

Vocabulary: Column vector - a mathematical representation showing horizontal and vertical movements using two numbers.

Example: A vector (-2) demonstrates movement 2 units left and downward.

Highlight: The top number in a column vector represents horizontal movement (positive for right, negative for left), while the bottom number shows vertical movement (positive for up, negative for down).

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Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

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Knowunity is the #1 education app in five European countries

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I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

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The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

What's a Column Vector? Easy Math Fun

user profile picture

Philippa Williams

@philippailliams_jwxn

·

3 Followers

Follow

The column vector mathematical concept explains vectors as quantities with magnitude and direction, represented through arrows and numerical components, forming a fundamental basis for mathematical calculations and spatial understanding.

  • Vectors are represented using column format with two numbers indicating horizontal and vertical movements
  • The vector scalar multiplication explanation shows how normal numbers (scalars) can modify vector components
  • The add column vectors method involves combining corresponding components of different vectors
  • Different notations exist for vectors including bold letters, underlined symbols, and arrow representations
  • Negative vectors maintain the same magnitude but move in opposite directions

09/09/2023

276

 

11/9

 

Maths

2

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

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Access to all documents

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Join milions of students

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Page 2: Vector Representations and Scalar Operations

This page covers various ways to represent vectors and introduces scalar multiplication. It explains how vectors can be written using different notations and how they interact with scalar values.

Vocabulary: Scalar - a regular number used to multiply vector components.

Example: When multiplying vector a=(2,4) by 2, the result is 2a=(4,8).

Highlight: A negative vector (-a) maintains the same magnitude as the original vector (a) but points in the opposite direction.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Vector Addition and Calculations

This page focuses on the process of adding column vectors and performing more complex vector calculations. The content demonstrates how to combine vectors through component-wise addition.

Definition: Vector addition involves adding corresponding components of two or more vectors.

Example: For vectors a=(3,5) and b=(2,11), their sum a+b=(5,16).

Highlight: Complex vector expressions can involve multiple operations including addition, subtraction, and scalar multiplication.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Vector Fundamentals Review

This page revisits the basic concepts of vectors, reinforcing the understanding of magnitude and direction. It provides additional examples of vector representation and movement.

Definition: Vectors represent quantities with both size (magnitude) and direction.

Example: Drawing vectors as arrows helps visualize their direction and magnitude.

Highlight: The column vector notation provides a precise way to specify both horizontal and vertical movements.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 5: Advanced Vector Operations

This page delves into more sophisticated vector operations and representations, expanding on scalar multiplication and directional concepts.

Example: Vector AB=(-3) represents movement from point A to point B.

Highlight: The direction of vector arrows is crucial for understanding the movement from one point to another.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 6: Complex Vector Calculations

This page concludes with advanced vector calculations, demonstrating how to perform multiple operations with vectors simultaneously.

Example: The calculation 2a-3b combines scalar multiplication and vector addition.

Highlight: Complex vector expressions can be solved by breaking them down into individual operations and following the order of operations.

Vectors
A vector is a quantity that has a magnitude (size) and
direction. Vectors are drawn as arrows.
magnitude
3
A column vector is one wa

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Introduction to Vectors and Column Vectors

This page introduces the fundamental concepts of vectors and their representation in column format. The content explains how vectors possess both magnitude and direction, visualized through arrows.

Definition: A vector is a quantity defined by both magnitude (size) and direction.

Vocabulary: Column vector - a mathematical representation showing horizontal and vertical movements using two numbers.

Example: A vector (-2) demonstrates movement 2 units left and downward.

Highlight: The top number in a column vector represents horizontal movement (positive for right, negative for left), while the bottom number shows vertical movement (positive for up, negative for down).

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

15 M

Pupils love Knowunity

#1

In education app charts in 12 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.