Vector Basics: Magnitude, Direction, and Properties

Vector Quality

• Magnitude and Direction: Vectors have both magnitude (amount of movement) and direction (orientation in space).
• Properties:
  • Can be added and subtracted using the head-to-tail method or parallelogram method.
  • Can be scaled (multiplied by a number).
  • Can be resolved into components (broken down into smaller vectors).
• Types of Vectors:
  • Displacement vectors: Represent the change in position of an object.
  • Velocity vectors: Represent the rate of change of displacement.
  • Acceleration vectors: Represent the rate of change of velocity.

Scalar Quality

• Magnitude only: Scalars have only magnitude (amount of something) but no direction.
• Properties:
  • Can be added and subtracted using simple arithmetic.
  • Can be scaled (multiplied by a number).
  • Do not have direction, so they cannot be resolved into components.
• Examples of Scalars:
  • Time
  • Temperature
  • Mass
  • Energy
  • Speed (note: speed is a scalar, while velocity is a vector)

Key Differences

• Vectors have direction, while scalars do not.
• Vectors can be resolved into components, while scalars cannot.
• Vectors require trigonometry and geometry to operate, while scalars use simple arithmetic.

Vector Quality

• Vectors have both magnitude (amount of movement) and direction (orientation in space).
• Vectors can be added and subtracted using the head-to-tail method or parallelogram method.
• Vectors can be scaled (multiplied by a number).
• Vectors can be resolved into components (broken down into smaller vectors).
• Displacement vectors represent the change in position of an object.
• Velocity vectors represent the rate of change of displacement.
• Acceleration vectors represent the rate of change of velocity.

Scalar Quality

• Scalars have only magnitude (amount of something) but no direction.
• Scalars can be added and subtracted using simple arithmetic.
• Scalars can be scaled (multiplied by a number).
• Scalars do not have direction, so they cannot be resolved into components.
• Examples of scalars include time, temperature, mass, energy, and speed.

Key Differences

• The main difference between vectors and scalars is that vectors have direction while scalars do not.
• Vectors can be resolved into components, while scalars cannot.
• Vectors require trigonometry and geometry to operate, while scalars use simple arithmetic.