Study Notes
Vectors are mathematical objects that have both magnitude and direction. They can be added, subtracted, and multiplied by scalars, but not divided.
- Vector — a quantity with both magnitude and direction. Example: The vector represents a movement 3 units right and 4 units up.
- Scalar — a real number that can multiply a vector. Example: Multiplying the vector by 3 gives .
- Column Vector — a way to represent vectors using vertical arrays. Example: represents a vector in 2D space.
- Position Vector — a vector that starts at the origin. Example: The position vector points from the origin to the point (4, -2).
- Magnitude — the length of a vector. Example: The magnitude of is 5.
Exam Tips
Key Definitions to Remember
- A vector has both magnitude and direction.
- A scalar is a real number used to multiply a vector.
- A position vector starts at the origin.
Common Confusions
- Confusing vectors with scalars, which only have magnitude.
- Forgetting that vectors cannot be divided.
Typical Exam Questions
- What is the magnitude of ? The magnitude is 5.
- How do you add vectors and ? The result is .
- What is the result of multiplying by 3? The result is .
What Examiners Usually Test
- Ability to perform vector addition and subtraction.
- Calculating the magnitude of a vector.
- Understanding and using position vectors.