Vectors in 3 Dimensions What is a 3-D vector? Vectors represent a movement of a certain magnitude (size) in a given directionYou should have already come across (2D) vectors at AS (see Basic Vector...
Problem Solving using Vectors Problem-solving with vectors Vectors can be used to prove two lines are parallel (see Vector Addition) They can also be used to show points are collinear (lie on the s...
Position Vectors What is a position vector? Position vectors describe the position of a point in relation to the origin They are different to direction vectors which describe the direction and dist...
Vector Addition Vector addition Adding vectors together lets us describes the movement between two points The single vector this creates is called the resultant vector Subtracting a vector is the s...
Magnitude & Direction What is the magnitude of a vector? The magnitude of a vector is simply its size It also tells us the distance between two points You can find the magnitude of a vector usi...
Basic Vectors What is a vector? Vectors represent a movement of a certain magnitude (size) in a given direction You should have already come across vectors when translating functions of graphs They...
x = g(x) Iteration What does xn + 1 = f(xn) mean? When an equation cannot be solved using the usual analytical methods, we can still find approximate solutions to a certain degree of accuracy Iter...
Change of Sign Failure When can the sign change method fail? There are certain circumstances where a change of sign fails to appropriately reflect the number or existence of roots If the interval i...
Change of Sign What does a change of sign mean? A sign change between f(a) to f(b) means there must be a root between a and b When an equation cannot be solved using the usual analytical methods, w...
