Introduction to Vectors

1
Introduction to Vectors

• AS Mathematics
• Mechanics 1 Module

2
Introduction

• Basics of vectors
• Vectors are values that show both magnitude
  (size) and direction
• A practical example of a vector is velocity which
  shows both the speed of an object and its
  direction
• Values that show only size are called scalar
  quantities
• At A level vectors are defined by orthogonal
  values of i and j, where i represents 1 unit in
  the x direction and j represents 1 unit in the y
  direction (if you use 3 dimensions then you can
  have k representing values in the z direction)
• Types of vector

3
Using vector mathematics

• Vectors can be added and subtracted from each
  other
• When you combine two or more vectors using i and
  j notation, you combine the is and js
  separately to then produce a resultant direction
• Eg. (3i 2j) (2i 5j) 5i 7j
• This can be shown as the parallelogram rule
• Example 1 Example 2
• Vectors can be increased or decreased by a given
  scale factor
• When scaling vectors, you just scale each
  component by the relevant scale factor
• Eg. 3 (3i 2j) 9i 6j
• Example 3

4
Using vector Mathematics II

• An important calculation is to be able to find
  the magnitude and angle of a given vector this
  is called resolving
• The Magnitude is found using Pythagorass
  Theorem, eg
• Magnitude of (ai bj) ?(a2b2)
• The Angle is found using Trigonometry
• Angle incline from horizontal of
• (ai bj) tan 1 (b/a)
• Resolving vectors

5
Exam Practice

• Qu. 1
• Qu. 2
• Qu. 3
• Qu. 4
• Qu. 5