Vectors

Vectors

Vectors

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 letters).
If a = (3) then the vector will look as follows:
(2)

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.

Example:
If a = (-5) and b = ( 2), find the magnitude of their resultant.
( 3) (1)
 

The resultant of two or more vectors is their sum.
The resultant therefore is (-3).
( 4)
The magnitude of this is 

(-3² + 4²) = 

(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.

Example:

Shape and Space

3D shapes

3D shapes

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Area

Area

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Circle theorems

Circle theorems

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Congruency

Congruency

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Coordinates

Coordinates

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Loci

Loci