2.1. Scalars and Vectors

• Scalars are physical quantities that have magnitude
• Vectors are represented using arrows
• The length of a vector arrow represents its magnitude
• What is the definition of displacement as an example of a vector?

  Change in position
• What does the length of a vector arrow in a diagram represent?

  Magnitude
• Arrows are useful for precise vector calculations.

  False
• Which physical quantity is an example of a vector?

  Velocity
• What does displacement measure in physics?

  Change in position
• Vectors only have magnitude.

  False
• The key difference between scalars and vectors is direction.


  True
• Scalars are fully described by a single numerical value.


  True
• What does the length of the arrow in a vector diagram represent?

  Magnitude
• The arrowhead of an arrow in a vector diagram indicates the direction of the vector.


  True
• To add two vectors graphically, place the tail of vector B at the head of vector A
• When subtracting vectors graphically, the reversed direction of vector B is added to vector A
• What is the approximate x-component of a vector with a magnitude of 10 units at an angle of 30°?

  8.66 units
• What is the formula for the vertical component of a vector?

  Magnitude × sin(angle)
• What is the vertical component of a vector with a magnitude of 10 units at 30°?

  5 units
• When a vector is multiplied by a negative scalar, its direction is reversed.


  True
• Unlike multiplying scalars, multiplying vectors by scalars affects their direction.
• What theorem is used to calculate the magnitude of the resultant vector in algebraic addition?

  Pythagorean theorem
• The magnitude and direction of the resultant vector are calculated in the same way for both vector addition and subtraction.

  True
• What are examples of scalars?

  Mass, time, temperature
• What are examples of vectors?

  Displacement, velocity, force
• Match the property with the correct quantity:

  Magnitude only ↔️ Scalars

  Magnitude and direction ↔️ Vectors
• Scalars have no direction.

  True
• Scalars have magnitude only, while vectors have both magnitude and direction
• Vectors can be visually represented using arrows
• Which property is unique to vectors compared to scalars?

  Direction
• Mass is an example of a scalar.


  True
• Vectors are physical quantities with both magnitude and direction
• Velocity is the rate of change of displacement with time
• Which property do vectors possess that scalars do not?

  Direction
• What property do scalars and vectors both have in common?

  Magnitude
• Steps to represent a vector using a diagram

  1️⃣ Draw an arrow

  2️⃣ Determine the length of the arrow for magnitude

  3️⃣ Determine the direction of the arrow
• In a coordinate system, vectors are represented by ordered pairs or sets of components
• A vector for a velocity of 20 m/s at an angle of 30 degrees to the horizontal would be an arrow with a length of 20
• The resultant vector in graphical vector addition is drawn from the tail of A to the head of B.


  True
• What are the two perpendicular vectors created when resolving a single vector?

  x-component and y-component
• What is the y-component of a vector with a magnitude of 10 units at an angle of 30°?

  5 units