Grade 10 · Core Mathematics · Lesson 2 of 21

Using Vector Notations in Different Ways

A Grade 10 Core Mathematics CBE lesson from the sub-strand Vectors I. In it, learners identify vectors expressed through standard notations including directed arrows, underlines, tildes below, and bold print.

Strand Measurements and GeometrySub-strand Vectors ILesson code 10CM-28-L240 minutes · 2 slides

KICD learning outcome (b)

Use vector notations in different ways.

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

Identify vectors expressed through standard notations including directed arrows, underlines, tildes below, and bold print.
Distinguish between vector notations and scalar expressions in mathematical problems.
Write single-letter and two-letter vectors correctly in handwritten work.

Key vocabulary

Vector notation: A standardised symbol or marking used to distinguish a vector quantity from a scalar.; Writing $\vec{C D}$ with an arrow above is a standard form of vector notation.
Tilde: A wavy line written below a letter to show that the letter represents a vector.; The symbol $\underset{\sim}{w}$ uses a tilde below the letter to represent a vector.
Scalar: A quantity that has magnitude or size only, with no associated direction.; The distance $J K = 15 cm$ is a scalar because it lacks directional notation.

Lesson preview

Slide 1 · Notation Conventions for VectorsOpening · 18 min

Figure 1: A diagram showing a directed line segment from point A to point B alongside four equivalent mathematical notations.

In mathematics, vectors require specific notations to distinguish them from scalar quantities. When representing a vector between two points, we write the starting and ending letters with a directed arrow above them, such as $\vec{A B}$ . When using single lowercase letters, vectors can be indicated by underlining the letter like $\underline{u}$ , placing a tilde beneath it like $\underset{\sim}{u}$ , or printing the symbol in bold type as $u$ . Recognising these notation forms ensures we correctly classify vector and scalar quantities in diagrams and calculations. Use Figure 1 to visualise the different ways we can write the same vector.

A directed vector from point $A$ to point $B$ is written with an arrow above as $\vec{A B}$ .
A single letter vector in handwriting is commonly underlined as $\underline{v}$ or written with a tilde below as $\underset{\sim}{v}$ .
Printed textbooks and digital displays often represent single letter vectors using bold type like $v$ .
Plain letters without an arrow, underline, tilde below, or bold text denote scalar quantities or ordinary distances.

Worked example. For two capital letters showing direction from point

X

to point

Y

, draw a right-pointing arrow above:

\vec{X Y}

. For a single lowercase letter

m

in written form, place a tilde beneath the letter:

\underset{\sim}{m}

or underline it:

\underline{m}

. For printed text, represent the single lowercase letter

m

in bold font:

m

. Answer: The notations are $\vec{X Y}$ , $\underset{\sim}{m}$ (or $\underline{m}$ ), and $m$ ..

Check question: Which of the following is the correct mathematical notation for a vector directed from point $P$ to point $Q$ ?

$\vec{P Q}$
$P Q$
$\vec{Q P}$
$\underline{P Q}$

Show answer

$\vec{P Q}$ . The standard mathematical convention for a vector directed from initial point $P$ to terminal point $Q$ uses a right-pointing arrow directly above the two capital letters, written as $\vec{P Q}$ .

Slide 2 · Identifying Vector and Scalar NotationsPractice · 22 min

Figure 2: A table categorising various mathematical symbols into vector and scalar notations based on their formatting.

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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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Using Vector Notations in Different Ways

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

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 21 lessons in Vectors I