Chapter 3 part 1 Vectors and Vector Addition

What are Component Vectors? Every Vector can be broken down into vectors which are entirely in the x & y directions (&z) These are its components vectors They can be found using “baby trig”

Finding a Vector from its components To find a vector given its components. Use the Pythagorean theorem to find magnitude And inverse tangent to find the angle

Adding Vectors Graphically The Sum of two vectors is called the Resultant. The Direction of the two vectors is as important to the magnitude of the resultant as their magnitudes! Vectors can be added through calculation or… Graphically To add vectors graphically : Draw each as an arrow proportionate in length to it magnitude, and in the right direction. Draw the 2nd vector beginning where the 1st ended Draw the Resultant from the beginning of the first to the end of the second Measure the resultant

Vector Model vs Vector Addition Diagrams Vector Model Diagrams Vector Graphic Addition diagrams Are used to add vectors graphically…thus The first starts at the object All others are draw from the point of the previous vector Are used to represent the vectors affecting an object…thus All vectors start at the object

Finding the Resultant by Calculation! Break each vector down into x & y-components. Add all x-components together to get the resultant’s X-component Add all y-components together to get the resultant’s Y-component Use the Pythagorean theorem to find the resultant’s Magnitude Use inverse tangent to find the resultant’s direction.