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VECTORS

CONTENT

(a) Vectors as directed line segment.

(b) Cartesian components of a vector.

(c) Magnitude of a vector, Equal vectors, Addition and subtraction of vectors, zero vectors, parallel vectors, multiplication of a vector by a scalar.

Vectors as directed line segment

A vector is any quantity which has direction as well as magnitude or size. Displacement, velocity, force, acceleration are all examples of vectors.

Since the points are on a Cartesian plane, AB can also be written as a column matrix, or column vector:

\(AB = a = \begin{pmatrix}4 \\ 2\end{pmatrix}\), Direction is important. BA is in the opposite direction to AB, although they are both parallel and have the same size: \(BA = -AB = -\begin{pmatrix}4 \\ 2\end{pmatrix} = \begin{pmatrix}-4 \\ -2\end{pmatrix}\)

A displacement vector is a movement in a certain direction without turning.

The vector ‘a’ is called the position vector of AB

Hence if a point has coordinates \((x , y)\), its position vector is \(\begin{pmatrix}x \\ y\end{pmatrix}\)

The figure shows the position vectors \(\overrightarrow{OA},\overrightarrow{OB}, \overrightarrow{OC}, \overrightarrow{OD} \)

In the figure above, the position vectors are as follows:

\(\overrightarrow{OA} = \begin{pmatrix}3 \\ 5 \end{pmatrix}, \overrightarrow{OB} = \begin{pmatrix}5 \\ -2 \end{pmatrix}, \overrightarrow{OC} = \begin{pmatrix}-3 \\ -4 \end{pmatrix}, \overrightarrow{OD} = \begin{pmatrix}-1 \\ 3 \end{pmatrix}\)

Class Activity:

Draw line segments to represent the following vectors.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS2 General Mathematics, SS2 General Mathematics Evaluation Questions, SS2 General Mathematics Evaluation Questions Third Term, SS2 General Mathematics Objective Questions, SS2 General Mathematics Objective Questions Third Term, SS2 General Mathematics Third Term
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