What are vectors?

• A vector is a type of number that has both a size and a direction. Example:- direction as a gradiant

and size as a value.

Gradient:- (x change, y change )

Size:- how far

• Here we only deal with two-dimensional vectors, although it is possible to have vectors with any number of dimensions

Vectors are represented as arrows, with the arrowhead indicating the direction of the vector, and the length of the arrow indicating the vector’s magnitude (ie its size )

A way of indicating vectors are by placing an arrow on top of the two letters and where the head is pointed is when the arrow is going too.

this is how the are written like there is no line between them by the way. i though they did

this is how the show the direction and the gradient of the line see the red writing that is the gradient

Note: ‘Vector’ is a word from Latin that means ‘carrier’

• In this case, the vector ‘carries’ shape A to shape B, so that meaning makes perfect sense!

Multiplying a vector by a scalar

• A scalar is a number with a magnitude but no direction – ie the regular numbers you are used to using

• When a vector is multiplied by a positive scalar, the magnitude of the vector changes, but its direction stays the same

• If the vector is represented as a column vector, then each of the numbers in the column vector gets multiplied by the scalar

this multiplying is based on the grid

and negative values are the vectors but in the opposite way.

Magnitude of a Vector

this is the change in x and why that is why they drew the triangle it is much easer to understand

Vectors have various uses in mathematics

• In mechanics, vectors represent velocity, acceleration and forces

• At IGCSE vectors are used in geometry – eg. translation

• Ensure you are familiar with the Revision Notes Vectors – Basics

these are applications

• Vectors have magnitude and direction

  • These notes look at finding the magnitude, or modulus, of a vector

  • Vectors are given in column vector form

This depends on the use of the vector

• For velocity, the magnitude would be speed

• For a force, the magnitude would be the strength of the force (in Newtons)

• The words magnitude and modulus mean the same thing with vectors

• In geometry magnitude and modulus mean the distance of the vector

  • This is always a positive value

  • The direction of the vector is irrelevant

  
  

• Magnitude or modulus is indicated by vertical lines

  • |a| would mean the magnitude of vector a

You can use Pythagoras’ Theorem! which is crazy and it will became much easier also.