1. Aims: To be able to calculate the magnitude of a vector. To be able to find the distance between two points. To be able to find a unit vector given it’s direction. Vectors Lesson 2

2. Finding the magnitude of a vector The m______________________ (or modulus) of a vector its length. We can calculate this using Pythagoras’s Theorem. For example, suppose we have the vector a A B The magnitude of this vector is written as or.

3. Finding the magnitude of a vector The magnitude of a 3D vector can also be found by applying Pythagoras’s Theorem. Has magnitude: For example, If we are given the coordinates of two points and we are asked to find the distance between them we again use Pythagoras’ Theorem in the same way. E.g. Find the distance between the points with coordinates P (–4, 7, –2) and Q (5, 9, –8). If d is the distance between the points then: d 2 = In general, if d is the distance between the points ( x 1, y 1, z 1 ) and ( x 2, y 2, z 2 ) then d 2 = ( x 2 – x 1 ) 2 + ( y 2 – y 1 ) 2 + ( z 2 – z 1 ) 2

4. magnitude of a vector on w/b

6. Unit vectors Remember, if the magnitude of a vector is 1 it is called a u________ vector. It is possible to find a unit vector parallel to any given vector, a, by dividing the vector by its magnitude. The unit vector parallel to the vector a is denoted by So, in general, Find a unit vector parallel to b = 4i – j + k

7. Now try the match up cards activity. Then ex 9B page 104, even numbers and 9C page 109 odd numbers. Find a unit vector parallel to b = 2i – j + 4k Unit vector on w/b

8. Trig Test – Good luck!