Vectors
Forms of Vectors
● Vectors have both direction and magnitude
● May be written in bold, underlined or 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
→ →
● AO = − OA
→ → → → → →
● AB = − OA + OB → AB = OB − OA
→
1 →
● Midpoint vector = OA + 2 AB
Forms of Vectors
● Vectors have both direction and magnitude
● May be written in bold, underlined or 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
→ →
● AO = − OA
→ → → → → →
● AB = − OA + OB → AB = OB − OA
→
1 →
● Midpoint vector = OA + 2 AB
