Vectors

Forms of Vectors
Vectors have both direction and magnitude
May be written in bold, underlinedor with an arrow above them to show
their direction
Magnitude-direction form:
Written in brackets
(magnitude, direction as angle)
Direction angle measured in anticlockwise direction from the
positive x-axis
(ie straight up is 90°)
Component form
Using unit vectors i and j (unit vector = magnitude of 1)
i is the unit vector in the x-direction
j is the unit vector in the y-direction
Written as a column vector
Total magnitude found by using pythagoras (with i and j being the
two sides of the triangle that aren’t the hypotenuse
If the magnitude is equal to r then i is equal to r cosθ and j is equal to
r sinθ

Vector Arithmetic
If you multiply a vector by a scalar, both i and j are multiplied by the scalar
Adding/Subtracting two vectors is done by adding/subtracting the i
components and the j components
Multiplying two vectors is hard and is covered in the matrices topic of
Further Maths

Position Vectors
A position vector is a vector which starts at the origin

Unit Vectors
Unit vectors have a magnitude of 1
Can find a unit vector which has the same direction as a given vector, a
To do:
Find the magnitude of the vector
Divide a by it’s magnitude
Unit vector called aˆ (a hat)