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Grade 10 · Core Mathematics · Lesson 21 of 21

Appreciating Vectors in Real-Life Situations

A Grade 10 Core Mathematics CBE lesson from the sub-strand Vectors I. In it, learners classify physical quantities as scalars or vectors based on magnitude and direction.

Strand Measurements and GeometrySub-strand Vectors ILesson code 10CM-28-L2140 minutes · 2 slides

KICD learning outcome (l)

Appreciate the use of vectors in real-life situations.

By the end of this lesson, learners should be able to

  1. Classify physical quantities as scalars or vectors based on magnitude and direction.
  2. Draw and represent directional real-life displacements geometrically and as column vectors.
  3. Calculate direct straight-line distances of combined perpendicular movements using Pythagoras' theorem.

Key vocabulary

Scalar quantity
A physical quantity that has magnitude or size only without any directional component.
A sack of maize with a mass of 50 kg is a scalar quantity.
Vector quantity
A physical measurement that possesses both magnitude and a specified direction in space.
Dropping a load vertically downward with a force of 100 N forms a vector quantity.
Column vector
A pair of numbers arranged vertically representing horizontal and vertical displacement components.
The column vector (−3050) represents 30 m West and 50 m North.
Displacement vector
A vector representing the shortest straight-line distance and direction from start to finish.
A swimmer going 30 m North then 40 m West achieves a resultant displacement.

Lesson preview

Slide 1 · Classifying Physical Quantities in Real-Life ContextsModel · 18 min
A thermometer and a bag of maize illustrate scalar quantities, while a weight on a pulley system shows downward displacement as a vector quantity.
Figure 1: A thermometer and a bag of maize illustrate scalar quantities, while a weight on a pulley system shows downward displacement as a vector quantity.

In real life, measurements are divided into scalar and vector quantities. A scalar quantity possesses magnitude only, such as temperature, mass, volume, or speed. In contrast, a vector quantity requires both magnitude and a specific direction to be fully defined, such as velocity, weight, force, and displacement. Understanding this distinction allows engineers, pilots, and farmers to accurately model forces and movements, such as a falling object dropping vertically downwards under gravity. Observe Figure 1 to see examples of everyday scalar and vector quantities.

  • Scalar quantities require only magnitude and appropriate units to be fully described.
  • Vector quantities require both magnitude and direction to describe physical effects accurately.
  • Quantities like mass, speed, and volume are scalars, whereas force, weight, and velocity are vectors.
  • Vertical drops under gravity illustrate vector displacements acting directly toward the centre of the Earth.
Worked example. 1. Scenario (a) specifies speed (60 km/h) without any given direction, so it is a scalar quantity. 2. Scenario (b) provides a magnitude (45 N) and a downward direction due to gravity, so it is a vector quantity. 3. Scenario (c) describes total distance covered along a path without a fixed direction, making it a scalar quantity. Answer: (a) Scalar quantity, (b) Vector quantity, (c) Scalar quantity..

Check question: A water pump draws water vertically upwards from a 15 m deep borehole, while a water tank holds a volume of 2 m3. Which statement correctly classifies these quantities?

  1. The 15 m displacement is a vector, and the 2 m3 volume is a scalar.
  2. The 15 m displacement is a scalar, and the 2 m3 volume is a vector.
  3. Both the 15 m displacement and the 2 m3 volume are vectors.
  4. Both the 15 m displacement and the 2 m3 volume are scalars.
Show answer

The 15 m displacement is a vector, and the 2 m3 volume is a scalar. Displacement specifies both distance (15 m) and a specific direction (vertically upwards), making it a vector quantity. Volume only has magnitude (2 m3) without direction, making it a scalar quantity.

Slide 2 · Representing Real-World Vectors and Calculating Net DisplacementsPractice · 22 min
A coordinate grid displays a vector journey of 50 metres North and 120 metres West, resulting in a 130-metre resultant displacement.
Figure 2: A coordinate grid displays a vector journey of 50 metres North and 120 metres West, resulting in a 130-metre resultant displacement.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • Both slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 20 lessons in this sub-strand
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All 21 lessons in Vectors I

  1. 1Explaining Vector and Scalar QuantitiesExplain vector and scalar quantities with illustrations
  2. 2Using Vector Notations in Different WaysUse vector notations in different ways
  3. 3Representing Vectors GeometricallyRepresent vectors geometrically in different situations
  4. 4Representing Vectors Geometrically in Different SituationsRepresent vectors geometrically in different situations
  5. 5Identifying Equivalent VectorsIdentify equivalent vectors in different situations
  6. 6Equivalent VectorsIdentify equivalent vectors in different situations
  7. 7Adding Vectors GeometricallyAdd vectors in different situations
  8. 8Adding Vectors Geometrically in Different SituationsAdd vectors in different situations
  9. 9Multiplying Vectors by ScalarsMultiply vectors by scalars
  10. 10Multiplying Vectors by Scalars: Graphical Construction and Scalar RatiosMultiply vectors by scalars
  11. 11Determining Column Vectors from Coordinates and DiagramsDetermine column vectors in different situations
  12. 12Determining Column Vectors and Vector ArithmeticDetermine column vectors in different situations
  13. 13Determining Position Vectors from the OriginDetermine position vectors in different situations
  14. 14Determining Position Vectors and Calculating Vector DisplacementsDetermine position vectors in different situations
  15. 15Calculating the Magnitude of a VectorWork out magnitude of a vector in different situations
  16. 16Working Out Vector Magnitudes in Different SituationsWork out magnitude of a vector in different situations
  17. 17Determining the Midpoint of a VectorDetermine the midpoint of a vector in different situations
  18. 18Determining Vector Midpoints and Endpoint CoordinatesDetermine the midpoint of a vector in different situations
  19. 19Determining Translation Vector as a TransformationDetermine translation vector as a transformation
  20. 20Determining Translation Vectors as TransformationsDetermine translation vector as a transformation
  21. 21Appreciating Vectors in Real-Life SituationsAppreciate the use of vectors in real-life situations