Summary
Vectors are mathematical objects that have both a magnitude and a direction, used to describe translations and construct geometric arguments. Scalars, on the other hand, have only magnitude and no direction.
- Vector — a quantity with both magnitude and direction. Example: Force, velocity, displacement.
- Scalar — a quantity with only magnitude and no direction. Example: Mass, volume, temperature.
- Column Vector — a vector represented with a top number for the horizontal component and a bottom number for the vertical component. Example: .
- Addition of Vectors — combining vectors by adding corresponding components or using the nose-to-tail method. Example: .
- Multiplication of Vectors — multiplying a vector by a scalar affects its magnitude and possibly its direction. Example: or .
- Parallel Vectors — vectors that have the same direction and proportional components. Example: and .
- Magnitude of a Vector — calculated using Pythagoras’ Theorem. Example: .
Exam Tips
Key Definitions to Remember
- Vector: A quantity with both magnitude and direction.
- Scalar: A quantity with only magnitude and no direction.
- Column Vector: A vector with horizontal and vertical components.
Common Confusions
- Mixing up vectors and scalars.
- Forgetting to change direction when multiplying by a negative scalar.
Typical Exam Questions
- What is a vector? A quantity with both magnitude and direction.
- How do you add vectors? By adding corresponding components or using the nose-to-tail method.
- How do you find the magnitude of a vector? Use Pythagoras’ Theorem.
What Examiners Usually Test
- Understanding of vector addition and subtraction.
- Ability to multiply vectors by scalars.
- Calculation of vector magnitude.