\(\blacksquare\) Vector quantity is any quantity that has both a magnitude and a direction.
\(\blacksquare\) Scalar quantity is a quantity that has magnitude but no direction.

\(\blacksquare\) A vector is usually represented by a directed line segment drawn as an arrow.

The length of the line represents the magnitude or the size of the vector and the arrow indicates the direction of the vector.

\(\blacksquare\) A vector from an initial point A to a terminal point B can be written as \(\overrightarrow{AB}\),  \(\utilde{a}\)\(AB\), or \(a\).

\(\blacksquare\) Vector \(-\overrightarrow{AB}\) represents a vector in the opposite direction as \(\overrightarrow{AB}\), that is \(\overrightarrow{BA}=-\overrightarrow{AB}\).
\(\blacksquare\) Two vectors are equal if and only if both the vectors have the same magnitude and direction.
\(\blacksquare\) A zero vector \(\utilde{0}\) has magnitude zero and its direction cannot be determined.

\(\blacksquare\) The vector \(\utilde{a}\) multiplied by the scalar \(k\) is also a vector and is written as \(k\utilde{a}\) where

(i) \( \begin{vmatrix} ka \end{vmatrix}=k \begin{vmatrix} ka \end{vmatrix}\)

(ii) if \(k \gt0\), then \(k\utilde{a}\) has the same direction as \(\utilde{a}\).

(iii) if \(k \lt0\), then \(k\utilde{a}\) has the opposite direction as \(\utilde{a}\).

\(\blacksquare\) Vector \(\utilde{a}\) and \(\utilde{b}\) are parallel if and only if \(\utilde{a}=k\utilde{a}\) where \(k\) is a constant.

Example 1:

Given the vector \(\utilde{m}\).



Express the vector below in term of \(\utilde{m}\).




Based on the given diagram,

the vector has twice the magnitude of the vector \(\utilde{m}\) and also due in same direction with vector \(\utilde{m}\).


Hence, the vector in term of \(\utilde{m}\) is




Example 2:

Given a pair of vector.

Determine whether the pair of vector is parallel or not.





Vector \(\utilde{a}\) and \(\utilde{b}\) are parallel if and only if \(\utilde{a}=k\utilde{b}\) where \(k\) is a constant.





\(\begin{aligned} \overrightarrow{FG}&=9(3\overrightarrow{EF})\\\\ &=27\overrightarrow{EF}. \end{aligned}\)

\(\therefore \overrightarrow{EF}\) and \(\overrightarrow{FG}\) are parallel.