Summary
Vectors are mathematical objects that represent both a direction and a magnitude, used to describe translations and construct geometric arguments. Scalars, on the other hand, have only magnitude.
- Vector — a quantity with both magnitude and direction Example: force, velocity, displacement
- Scalar — a quantity with only magnitude Example: mass, volume, temperature
- Addition of Vectors — combining vectors using the parallelogram rule or nose-to-tail method Example: a + b
- Multiplication of Vectors — scaling a vector by a scalar Example: 2x or -3x
- Column Vector — a vector represented with horizontal and vertical components Example: (5, 3)
- Parallel Vectors — vectors with the same direction and proportional components Example: vectors a and b are parallel if a = kb
- Magnitude of a Vector — calculated using Pythagoras' Theorem Example: |a|
Exam Tips
Key Definitions to Remember
- Vector: a quantity with both magnitude and direction
- Scalar: a quantity with only magnitude
- Column Vector: a vector with horizontal and vertical components
Common Confusions
- Mixing up vectors and scalars
- Forgetting to add vectors component-wise
Typical Exam Questions
- How do you add two vectors? Use the parallelogram rule or nose-to-tail method
- What is the result of multiplying a vector by a scalar? The vector is scaled by the scalar
- How do you determine if two vectors are parallel? Check if their components are proportional
What Examiners Usually Test
- Understanding of vector addition and subtraction
- Ability to multiply vectors by scalars
- Calculation of vector magnitude using Pythagoras' Theorem