Grade 10 · Core Mathematics · Lesson 4 of 21

Representing Vectors Geometrically in Different Situations

A Grade 10 Core Mathematics CBE lesson from the sub-strand Vectors I. In it, learners represent vector quantities geometrically using directed line segments, scale factors, and compass directions.

Strand Measurements and GeometrySub-strand Vectors ILesson code 10CM-28-L440 minutes · 2 slides

KICD learning outcome (c)

Represent vectors geometrically in different situations.

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

Represent vector quantities geometrically using directed line segments, scale factors, and compass directions.
Interpret scale drawings to determine the magnitude and compass direction of a given vector in real-life contexts.

Key vocabulary

Directed Line Segment: A straight line segment having a specified length and an arrowhead indicating direction.; The vector $\vec{P Q}$ is represented by a directed line segment of length four centimetres.
Scale Factor: The ratio comparing a length on a diagram to the actual physical distance.; Using a scale factor of one centimetre to five metres, ten metres equals two centimetres.
Compass Direction: A direction specified relative to cardinal points such as North, South, East, or West.; The displacement vector points in the compass direction of North-West at forty-five degrees.

Lesson preview

Slide 1 · Geometrical Representation of VectorsModel · 18 min

Figure 1: A compass rose showing a 4 centimetre vector pointing North-East, alongside a 6 centimetre vector directed due South from point P to Q.

To represent vectors geometrically in physical contexts, we combine scale drawings with directional references such as compass bearings. A directed line segment uses its scaled length to depict the magnitude of a physical quantity like displacement or velocity. The arrow indicates the precise direction, such as due South or North-East. By setting a clear scale and drawing cardinal directions, any vector quantity can be accurately portrayed and visually interpreted.

A vector is drawn as a straight line segment with a specific length and an arrow indicating direction.
Scale factors convert real-life magnitudes into measurable centimetres on paper or grid drawings.
Compass directions like North, South, North-East, and South-West set the precise orientation of the vector.
The terminal arrowhead indicates the direction of motion or displacement from the initial starting point.

Worked example. Choose a scale where

1 cm = 3 km

, so

12 km

is represented by a line segment of length

\frac{12}{3} = 4 cm

. Draw a reference compass rose showing North, East, South, and West axes. Draw a straight line at an angle of

45^{\circ}

North of East (NE) starting from the origin point

O

. Measure a segment of length

4 cm

along this line and mark the terminal end with a directional arrow. Answer: A directed line segment measuring $4 cm$ at $45^{\circ}$ North of East, terminated by a directional arrow towards NE..

Check question: A vector $\vec{w}$ is drawn on a grid pointing due South with a length of $5 cm$ . If the scale is $1 cm = 10 m$ , state the magnitude and compass direction represented by $\vec{w}$ .

$50 m$ due South
$5 m$ due South
$0.5 m$ due South
$50 m$ due North

Show answer

$50 m$ due South. The drawn length of $5 cm$ represents $5 \times 10 m = 50 m$ . The arrow points directly downwards, which corresponds to the due South direction stated.

Slide 2 · Representing Vectors in Real-Life ContextsPractice · 22 min

Figure 2: Two vector diagrams showing a 4 centimetre vector pointing South-West, and a 3 centimetre vertical vector pointing downwards to a horizontal line.

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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