1.2.2 Representing vectors graphically

• If you kick a soccer ball, what two aspects are considered vectors?

  Speed and direction of the kick
• If the arrow was pointing to the left, what would that indicate about the direction on the coordinate plane?

  Negative direction
• How does the direction of the arrow relate to the positive and negative values on the coordinate plane?

  The arrow points in the positive direction on the coordinate plane
• In a graph, what does the angle from the x-axis indicate?

  The direction of the vector
• How is the direction of a vector measured?

  As the angle from a fixed reference point
• What does the magnitude of a vector represent?

  Length of the arrow
• How do the components of a vector combine?

  They form the overall vector magnitude
• What are vectors defined as?

  Measurements with magnitude and direction
• How does the length of an arrow relate to vector magnitude?

  A longer arrow indicates a larger magnitude
• What are the two main components of a vector?

  • Magnitude: represented by the length of the arrow
  • Direction: measured as the angle from a fixed reference point
• If a vector has a length of about 6 units, what does this represent?

  The magnitude of the vector
• What is the name of the axis labeled 'y-axis'?

  y-axis
• If a car is moving eastward, where would the arrowhead of its vector point?

  It would point east
• What does the magnitude of a vector represent?

  The size or strength of the vector
• What is the name of the axis labeled 'x-axis'?


  x-axis
• What do the horizontal and vertical components represent in this coordinate system?

  The horizontal component and the vertical component
• How can you use this coordinate system to describe the position of an object?

  • Specify the x-coordinate (horizontal position)
  • Specify the y-coordinate (vertical position)
  • The object's location is defined by the intersection of the x and y values
• What are the components of a vector?

  • Horizontal component
  • Vertical component
• How does scaling affect the representation of a vector's magnitude?

  It reflects the magnitude by the arrow's length
• What is the value of the x-coordinate at the point where the arrow is pointing?

  3
• What does the direction of a vector indicate?

  The direction the vector points
• What does the symbol of a vector represent?

  A letter (often bold) representing the vector
• Why are vectors important in physics?

  They describe speed and acceleration
• How is the direction of a vector represented?

  By the angle from a reference point
• What is the main difference between scalar and vector quantities?

  • Scalars have magnitude only.
  • Vectors have both magnitude and direction.
• What are the key differences between magnitude and direction in vectors?

  • Magnitude:
  • Meaning: Size or strength of the vector
  • Representation: Length of the arrow
  • Example: Speed of a car (60 km/h)

  
  

  • Direction:
  • Meaning: Direction the vector points
  • Representation: Angle from a reference point
  • Example: Eastward movement of a car
• What do scalar quantities have?

  Only magnitude
• What does an arrowhead on a vector indicate?

  It indicates the direction of the vector
• What does the arrow in the image represent?

  • The arrow represents the positive direction on the coordinate plane
• Why is properly scaling vectors important?

  For accurate and clear graphical representation
• How does the arrowhead of a vector relate to an object's movement?

  It points in the direction the object is moving
• Why is it important to label vectors with both magnitude and symbol?

  It ensures clarity when discussing the vector
• What is the direction shown in the image?

  Positive
• How can you determine the x-coordinate of the point where the arrow is pointing?

  • The x-coordinate can be determined by reading the value on the x-axis at the point where the arrow is pointing
• Compare the properties of scalar and vector quantities.

  | Property | Scalar | Vector |

  |---|---|---|

  | Magnitude | Yes | Yes |

  | Direction | No | Yes |
• What are the two components used to label vectors?

  Magnitude and symbol
• If a force of 50 N is represented by a 5 cm arrow, how long would the arrow be for a force of 100 N?

  10 cm
• What is the relationship between force and arrow length in vector representation?

  • Each centimeter corresponds to a specific force
  • Example: 50 N = 5 cm (10 N/cm)
  • Example: 100 N = 10 cm
  • Example: 150 N = 15 cm
• What information about the coordinate plane can be inferred from the image?

  • The image shows a coordinate plane with positive and negative values on the x-axis
  • The arrow points in the positive direction on the coordinate plane
• What is the length of a vector representing a 50 N force if drawn 5 cm long?

  5 cm