Vectors
Overview
A delivery drone needs more than a distance to reach its target: it needs a direction too. Fly 4 km the wrong way and you are further from the parcel than when you started. Vectors are the tool mathematics uses to carry size and direction together, and they turn awkward geometry problems, where a diagram only gets you so far, into clean algebra.
This topic builds vector notation and column vectors from the ground up, covers addition, subtraction, scalar multiplication and magnitude, and finishes with the technique examiners favour most: using vectors to prove that lines are parallel, that points are collinear, and that several lines meet at a single point.
Objectives
- Understand scalar and vector quantities in two dimensions
- Understand and use vector notation including column vectors
- Represent a vector by a directed line segment
- Understand and use parallel vectors, unit vectors and position vectors
- Find the sum and difference of two vectors
- Calculate the modulus (magnitude) of a vector
- Multiply a vector by a scalar
- Find the resultant of two or more vectors
- Apply vector methods to simple geometrical problems including collinearity, parallel lines and concurrency
Mind map
This topic is mapped out so you can see how the ideas connect.
Open the mind map in the app
Flashcards
Quick recall practice on the facts this topic is tested on.
Practise these cards in the app
Lesson Note
Complete Note Available on the Green Bridge App
Get the Green Bridge CBT app on your phone or computer for the complete IGCSE library: past papers, mark schemes, mind maps, flashcards and audio lessons.
Lesson Evaluation
Congratulations on completing the lesson on Vectors. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- Which of these is a vector quantity? A) Mass B) Temperature C) Velocity D) Area Answer: C
- What is the magnitude of the vector (8, -6)? A) 2 B) 10 C) 14 D) 100 Answer: B
- If a = (5, -2) and b = (-3, 6), what is a - b? A) (2, 4) B) (8, -8) C) (-8, 8) D) (2, -4) Answer: B
- Multiplying a vector by -3 will: A) triple its magnitude and keep the same direction B) triple its magnitude and reverse its direction C) divide its magnitude by 3 and reverse its direction D) keep the magnitude the same and reverse its direction Answer: B
- P, Q and R have position vectors such that PQ = 2(PR). What can you conclude? A) P, Q and R are collinear B) PQ is perpendicular to PR C) Q is the midpoint of PR D) Nothing can be concluded Answer: A
Work through these questions in the app
Work through these questions in the app
Recommended Books
Practice Mock Questions
Want to practice mock questions on Vectors? Download the Green Bridge CBT app to access mock questions and full practice assessments for this topic.
Download The App On Google Playstore
Everything you need to excel in your exams
