Vectors
Watch this video to learn about vectors
Geometry
A A vector describes a movement from one point to another. A vector quantity has magnitude (size) and direction. describes a movement from one point to another.
Vector notation
A vector quantity has both direction and The magnitude tells us the size of the vector. (size).
(In contrast a scalar quantity has magnitude only - eg, the numbers 1, 2, 3, 4...)
This arrow represents a vector. The direction is given by the arrow, while the length of the line represents the magnitude. The vector components are \(\left( \begin{array}{l} 3\\ 4 \end{array} \right)\)
This vector can be written as: \(\overrightarrow {AB}\) , a, or \(\left( \begin{array}{l} 3\\ 4 \end{array} \right)\).
In print, a is written in bold type. In handwriting, the vector is indicated by putting a line underneath the letter: \(\underline a\)
Example
Write down the 3 ways to describe the vector if the arrow is now pointing from B to A.
Answer
Remember that the arrow describes the direction. So, in this case, the vector is from B to A. If we move 'backwards' along a vector, it becomes negative, so a becomes -a. Moving from B to A entails moving 3 units to the left, and 4 down.
So the three ways to write this vector are: \(\overrightarrow {BA}\), \(-a\) and \(\left( \begin{array}{l} - 3\\ - 4 \end{array} \right)\).
More guides on this topic
- Determine the gradient of a straight line
- Circle geometry
- Calculating the volume of a standard solid
- Applying Pythagoras Theorem
- Applying the properties of shapes to determine an angle
- Using similarity
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates