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What's a Column Vector? Easy Math Fun

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Philippa Williams

09/09/2023

Maths

vectors

What's a Column Vector? Easy Math Fun

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

466

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=2,42,4 by 2, the result is 2a=4,84,8.

Highlight: A negative vector a-a maintains the same magnitude as the original vector aa 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=3,53,5 and b=2,112,11, their sum a+b=5,165,16.

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 magnitudemagnitude 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=3-3 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.

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Maths

466

9 Sept 2023

6 pages

What's a Column Vector? Easy Math Fun

user profile picture

Philippa Williams

@philippailliams_jwxn

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... Show more

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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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=2,42,4 by 2, the result is 2a=4,84,8.

Highlight: A negative vector a-a maintains the same magnitude as the original vector aa 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 contentIt'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=3,53,5 and b=2,112,11, their sum a+b=5,165,16.

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 contentIt'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 magnitudemagnitude 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 contentIt'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=3-3 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 contentIt'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 contentIt'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 sizesize and direction.

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

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

Highlight: The top number in a column vector represents horizontal movement positiveforright,negativeforleftpositive for right, negative for left, while the bottom number shows vertical movement positiveforup,negativefordownpositive for up, negative for down.

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This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

Best app on earth! no words because it’s too good

Thomas R

iOS user

Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.

Basil

Android user

This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.

Rohan U

Android user

I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.

Xander S

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now

Paul T

iOS user