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A vector is a quantity that has a magnitude (length) and a direction.
Example: Displacement, velocity and acceleration.
Vectors are often described using column vector.
Vectors are often named using letter a, b, c, etc.
The letters are usually underlined if written by hand, but they are in bold type in examination papers.
When you multiply a vector by an ordinary number, k:
To find he negative of a vector, reverse the sign of the numbers.
You can add and subtract two vectors using simple arithmetic.
The magnitude of a is the length.
We can use Pythagoras’ theorem to find it.
AB = AO + OB
Ratio and Vectors:
If X is the point on AB for which AX : XB = 2 : 1, this means that AX is twice as long as XB.
Therefore, AX is two-thirds of the way along AB.
Proof 1: Parallel Line
Condition: If AB = k CD, AB and CD are parallel.
For example, 6a + 3b is parallel to 2a + b, since 6a + 3b = 3 x (2a + b)
Proof 2: Straight Line
Condition 1: If AB = k CD, AB and CD are parallel.
Condition 2: Since both AB and BC go through common point B, therefore ABC is a straight line.
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