2.3.1 Scalars and Vectors

• Scalars are quantities that have magnitude only, without any direction.
• Vectors are quantities that have both magnitude and direction.
• Which scalar quantity is measured in kilograms?

  Mass
• What is the SI unit for energy?

  Joules
• Vectors only have magnitude, no direction.

  False
• What is the unit of temperature in the SI system?

  Kelvin
• What is the magnitude of velocity measured in?

  m/s
• Match the vector quantity with its example:

  Velocity ↔️ 25 m/s North

  Force ↔️ 10 N Downwards

  Displacement ↔️ 5 meters East

  Acceleration ↔️ 2 m/s² West
• The length of a vector arrow corresponds to its magnitude.


  True
• An arrow diagram helps visualize both the magnitude and direction of a vector


  True
• Vectors can be added graphically by placing them tip-to-tail
• A force vector of 10 N at a 30° angle above the horizontal has a vertical component of approximately 5.0 N
• Give an example of a vector quantity that includes both magnitude and direction.

  Velocity
• Vectors are physical quantities that possess both magnitude and direction
• What are some examples of scalar quantities?

  Mass, time, temperature
• What are some examples of vector quantities?

  Displacement, velocity, force
• Vectors are quantities that possess both magnitude and direction.
• Scalars are described by magnitude only, while vectors require both magnitude and direction.
• Scalars are fully described by their magnitude without direction.


  True
• Scalar quantities are fully described by their numerical value
• The key difference between vectors and scalars is that vectors have an associated direction
• Vectors require both magnitude and direction, whereas scalars only need a numerical value
• Vectors are commonly represented using arrows
• How is the magnitude of a vector represented in an arrow diagram?

  Length of the arrow
• What are the two components of a velocity vector called when broken down along axes?

  Horizontal and vertical
• What is the single vector called that represents the combined effect of multiple vectors added graphically?

  Resultant vector
• What is the key difference between scalars and vectors?

  Direction
• Vectors are represented using arrows where the length indicates magnitude and the direction indicates direction


  True
• The length of an arrow representing a vector corresponds to its magnitude.

  True
• Match the scalar quantity with its example:

  Time ↔️ 5 seconds

  Temperature ↔️ 25°C

  Speed ↔️ 30 m/s
• Scalars require both magnitude and direction to be fully defined.

  False
• How is the magnitude of a vector represented using an arrow?

  Length of the arrow
• The horizontal component of a velocity vector has a magnitude of 20 m/s and a direction of East.
• What are the two primary methods for adding vectors?

  Graphical and component methods
• Which method is more precise for adding vectors in complex scenarios?

  Component method
• Steps for subtracting vectors graphically

  1️⃣ Draw the first vector A from the origin

  2️⃣ Reverse the direction of the second vector B to -B

  3️⃣ Place the tail of -B at the tip of A

  4️⃣ Draw the resultant vector from the origin to the tip of -B
• Component subtraction is precise but requires understanding of trigonometry
• Multiplying a vector by a positive scalar increases its magnitude
• Vectors possess both magnitude and direction.


  True
• Scalars have both magnitude and direction.

  False