1.1 representation of Vectors
A vector can be represented by a directed line segment as shown on the left. The direction of the line segment OA (on a bearing of 60¢X) is the direction of the vector and the length OA represents the magnitude of the vector.
If the line is labeled AB, the vector it represents is written AB. The order of the letters indicates the direction of the vector.
¡÷
(the vector BA is represented by the same line but in the opposite direction)
alternatively, a single lower case letter in the middle of the line can be used. In this case there must be an arrow on the line to show the direction of the vector.
In print the letter is set in bold type, e.g. a.
For hand written work, use a or a
ƒj
The magnitude of a is written as a
Related vectors.
Two vectors are equal if they have equal magnitudes and the same direction.
We write a = b
If the direction of b is reversed then a and b are equal and opposite
We write a = -b
If two vectors have the same direction but different magnitudes then one can be expressed as a multiple of the other, e.g.
b = 2a and q = 3p
In general, if a and b are parallel then a = kb where k is a constant of proportion and is scalar.
¡÷ ¡÷
For example, if AB represents a vector p, then 1/3 p is represented by AC where AC = 1/3AB and 2p is
¡÷
presented by AD where AB is extended so that AD = 2AB.
Addition of vectors
Consider what happens if hiker starts from the corner of A of a field, walks for 30m beside the hedge along one side to B and then 40m along the side perpendicular to the first, to C. the hiker could have reached the same point C by walking directly across the field (assuming this to be allowed).
