Grade 10 · Core Mathematics · Lesson 5 of 21

Identifying Equivalent Vectors

A Grade 10 Core Mathematics CBE lesson from the sub-strand Vectors I. In it, learners determine the magnitude and direction of vectors on a grid.

Strand Measurements and GeometrySub-strand Vectors ILesson code 10CM-28-L540 minutes · 2 slides

KICD learning outcome (d)

Identify equivalent vectors in different situations.

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

Determine the magnitude and direction of vectors on a grid.
Identify equivalent vectors across different geometric positions.

Key vocabulary

Magnitude: The overall length or size of a vector quantity regardless of direction.; Vector $a$ has a magnitude of $5$ units on the square grid scale.
Direction: The line along which a vector points, indicated by an arrow or compass angle.; Vector $w$ (4 squares up) has a direction pointing due North on the grid.
Equivalent vectors: Vectors that possess identical magnitude and point in the exact same direction.; Vectors $p$ and $s$ are equivalent because both equal $(\begin{array}{c} 2 \\ 3 \end{array})$ .

Lesson preview

Slide 1 · Comparing Magnitudes and Directions of Grid VectorsOpening · 18 min

Figure 1: A Cartesian plane displaying four vectors, labelled a, b, c, and d, plotted on a grid to compare their magnitudes and directions.

To identify equivalent vectors in different situations, we compare their geometric properties on a grid. Every vector possesses both a length, called magnitude, and an orientation, called direction. By counting horizontal and vertical grid squares, or using compass directions, we determine whether two vectors share identical magnitudes, identical directions, or both. Vectors with equal magnitude and direction represent the exact same change in position.

A vector on a grid has magnitude representing its length and an arrow specifying direction.
We determine magnitude by measuring length or applying Pythagoras to the grid displacement components.
Vectors pointing along parallel lines in the same arrow orientation share identical directions.
Comparing magnitude and direction allows us to group vectors with similar geometric properties.

Worked example. 1. Calculate magnitude of vector

u

∣ u ∣ = \sqrt{4^{2} + 3^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5 km

. 2. Determine direction of vector

u

4

km East and

3

km North gives a bearing of

{053.13}^{\circ}

(or

N {53.13}^{\circ} E

). 3. Calculate magnitude of vector

v

∣ v ∣ = \sqrt{4^{2} + 3^{2}} = \sqrt{25} = 5 km

. 4. Determine direction of vector

v

4

km East and

3

km North gives the same bearing of

{053.13}^{\circ}

. Answer: Both vectors $u$ and $v$ have a magnitude of $5 km$ and point in the direction $N {53.13}^{\circ} E$ ..

Check question: Vector $m$ moves 3 units East and 4 units North. Vector $n$ moves 4 units East and 3 units North. Which statement is true about vectors $m$ and $n$ ?

They have the same magnitude but different directions.
They have the same direction but different magnitudes.
They have both the same magnitude and the same direction.
They have different magnitudes and different directions.

Show answer

They have the same magnitude but different directions. Both vectors have a magnitude of $\sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5 units$ . However, vector $m$ moves 3 units East and 4 units North, while vector $n$ moves 4 units East and 3 units North, meaning they point in different directions.

Slide 2 · Defining and Identifying Equivalent VectorsPractice · 22 min

Figure 2: A coordinate grid displaying five vectors, labelled p, q, r, s, and t, used to identify which ones are equivalent.

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

See the school projector WhatsApp us