Vectors, Glossary

Knowing the vocabulary of Vectors precisely is worth easy marks in SPM Add Math. Questions often turn on a single keyword, read it correctly and the method follows; misread it and even good algebra earns nothing.

Because the SPM paper is bilingual (BM/EN), each term below shows the English and Malay wording, so your child recognises it whichever way a question is phrased.

• Scalar, A scalar is a quantity that has only size (magnitude) and no direction, such as mass, length, temperature, or speed. Scalars are described by a single number with a unit. They contrast with vectors, which also carry a direction, and they obey ordinary arithmetic. →
• Vector, A vector is a quantity with both magnitude and direction, such as displacement, velocity, or force. It is often drawn as a directed line segment and written $\vec{AB}$ or in bold. Two vectors are equal only when they share the same magnitude and direction. →
• Magnitude of a Vector, The magnitude of a vector is its length, always a non-negative number. For a vector $x\mathbf{i}+y\mathbf{j}$ in the Cartesian plane it is $\sqrt{x^{2}+y^{2}}$, found using Pythagoras' theorem. It is written with modulus bars, as $|\vec{AB}|$. →
• Unit Vector, A unit vector is a vector with magnitude exactly one, used to indicate direction. Any non-zero vector $\mathbf{a}$ has a unit vector $\hat{\mathbf{a}}=\frac{\mathbf{a}}{|\mathbf{a}|}$ in the same direction. In the plane, $\mathbf{i}$ and $\mathbf{j}$ are the unit vectors along the axes. →
• Resultant Vector, A resultant vector is the single vector that results from adding two or more vectors, representing their combined effect. Geometrically it is found by joining vectors head to tail, or by the parallelogram law. In component form, we simply add the corresponding $\mathbf{i}$ and $\mathbf{j}$ parts. →
• Parallel Vectors, Two vectors are parallel when one is a scalar multiple of the other, written $\mathbf{a}=k\mathbf{b}$ for some number $k$. They point in the same or exactly opposite directions. This test is useful for showing that three points are collinear, lying on one straight line. →
• Position Vector, A position vector gives the location of a point relative to the origin, so point $A$ has position vector $\vec{OA}$. Using position vectors, the vector from $A$ to $B$ is $\vec{AB}=\vec{OB}-\vec{OA}$. They turn geometric points into vectors we can compute with. →

Do not just memorise definitions, practise using each term inside a full solution, the way a marker expects to see it. In the Vectors chapter especially, stating the right definition or condition in your working can itself earn a method mark.

Our teachers check that a student can both recall a term and deploy it fluently under exam conditions.

Vocabulary sticks best when it is tied to doing rather than reading. Instead of learning the Vectors terms as a flat list, meet each one inside a worked question and say the step aloud in words as you write it, a term you can use in a sentence is a term you understand.

It also helps to link related terms together rather than in isolation, since Vectors questions usually combine several ideas at once. Because the SPM paper is bilingual, glance once at the Malay and English wording of each term side by side, so the language a question is set in never throws you.

If a term keeps feeling slippery, that is usually a sign the underlying idea needs another look, not the word itself, and that is exactly the kind of gap a one-to-one lesson closes quickly.