A vector quantity has both length (magnitude) and direction.
The opposite is a scalar quantity, which only has magnitude. Vectors can be
denoted by AB, a, or AB (with an arrow above the
If a = then the vector will look as follows:
NB1: When writing vectors as one number above another in
brackets, this is known as a column vector.
NB2: In textbooks and here,
vectors are indicated by bold type. However, when you write them, you need to
put a line underneath the vector to indicate it.
Multiplication by a Scalar
When multiplying a vector by a scalar (i.e. a number), multiply each
component of the vector by that number.
If a = , and b = 2a, sketch a and b.†
† † ††
If a = , then† 2a =
If a = and b = , find the magnitude of their resultant.
resultant of two or more vectors is their sum.
The resultant therefore is
magnitude of this is ÷(-3≤ + 4≤) =
÷(9 + 16) = ÷(25) = 5
The addition and subtraction
of vectors can be shown diagrammatically. To find a + b, draw
a and then draw b at the end of a. The resultant is the
line between the start of a and the end of b.
To find a
- b, find -b (see above) and add this to a.
A unit vector has a magnitude of 1. The unit vector in the direction of the
x-axis is i and the unit vector in the direction of the y-axis is
j. For example on a graph, 3i + 4j would be at (3 , 4).
This method is another method of writing down vectors. It also makes adding and
subtracting vectors easy: you just add the i terms together and add the
j terms together.
For example: 3i + j †plus †5i -
4j = † 8i - 3j.†
This is the same as writing is as:
Copyright © Matthew Pinkney 2003