1. Introduction to Vectors AS Mathematics Mechanics 1 Module

2. Introduction : 4 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) 4 Types of vector Types of vector

3. Using vector mathematics 4 Vectors can be added and subtracted from each other –When you combine two or more vectors using i and j notation, you combine the i’s and j’s separately to then produce a resultant direction Eg. (3i + 2j) + (2i + 5j) = 5i + 7j –This can be shown as the parallelogram rule –Example 1Example 2Example 1Example 2 4 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 3Example 3

4. Using vector Mathematics II 4 An important calculation is to be able to find the magnitude and angle of a given vector – this is called resolving 4 The Magnitude is found using Pythagoras’s Theorem, eg –Magnitude of (ai +bj) =  (a 2 +b 2 ) 4 The Angle is found using Trigonometry –Angle incline from horizontal of (ai + bj) = tan –1 ( b / a ) 4 Resolving vectors Resolving vectors

5. Exam Practice 4 Qu. 1 Qu. 1 4 Qu. 2 Qu. 2 4 Qu. 3 Qu. 3 4 Qu. 4 Qu. 4 4 Qu. 5 Qu. 5