• 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.
• A vector from an initial point \(A\) to a terminal point \(B\) can be written as \(\overrightarrow{AB}\), \(\utilde{a}\), \(AB\) or \(a\).
• Vector \(-\overrightarrow{AB}\) represents a vector in the opposite direction as that is \(\overrightarrow{AB}\), such that \(\overrightarrow{BA}=-\overrightarrow{AB}\).
• Two vectors are equal if and only if both the vectors have the same magnitude and direction.

•  A zero vector \(\utilde{0}\) has magnitude zero and its direction cannot be determined.

•  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 \(\utilde{a}\).

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

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:

\(2\utilde{m}\).

Given a pair of vector.

Determine whether the pair of vector is parallel or not.

\(\overrightarrow{EF}=\dfrac{1}{3}\utilde{r}\)

\(\overrightarrow{FG}=9\utilde{r}\)

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

 \(\overrightarrow{EF}=\dfrac{1}{3}\utilde{r}\),

Then,

\(\utilde{r}=3\overrightarrow{EF}\).

Hence,

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

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

• 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.
• A vector from an initial point \(A\) to a terminal point \(B\) can be written as \(\overrightarrow{AB}\), \(\utilde{a}\), \(AB\) or \(a\).
• Vector \(-\overrightarrow{AB}\) represents a vector in the opposite direction as that is \(\overrightarrow{AB}\), such that \(\overrightarrow{BA}=-\overrightarrow{AB}\).
• Two vectors are equal if and only if both the vectors have the same magnitude and direction.

•  A zero vector \(\utilde{0}\) has magnitude zero and its direction cannot be determined.

•  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 \(\utilde{a}\).

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

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:

\(2\utilde{m}\).

Given a pair of vector.

Determine whether the pair of vector is parallel or not.

\(\overrightarrow{EF}=\dfrac{1}{3}\utilde{r}\)

\(\overrightarrow{FG}=9\utilde{r}\)

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

 \(\overrightarrow{EF}=\dfrac{1}{3}\utilde{r}\),

Then,

\(\utilde{r}=3\overrightarrow{EF}\).

Hence,

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

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