1. Component of vector A along the direction of B A B Project A onto B: Drop perpendiculars to B This component is positive A B This component is negative

3. Sometimes only one perpendicular needs be dropped: A B A Weight of object on an incline B Choose B to point down incline

4. Special Cases 5 A B Component = +5 A B 3 3 Component = -3 5 A B Component = 0

5. X- and y- components x y A AxAx AyAy

6. How to calculate components x A 1. Make component part of a triangle containing A 2. Identify an angle in the triangle 3. Use trig to find length of component: sine or cosine? Adjacent. Therefore cosine. Length of component =5cos30°=5×0.866=4.33 4. Add appropriate sign: X-Component = - 4.33 5

7. How to calculate components x A 1. Make component part of a triangle containing A 2. Identify an angle in the triangle 3. Use trig to find length of component: sine or cosine? Opposite. Therefore sine. Length of component =5sin60°=5×0.866=4.33 4. Add appropriate sign: X-Component = - 4.33 5 5

8. Component of sum=sum pf components x y A B C=A+B CxCx AxAx BxBx C x =A x +B x C y =A y +B y

9. Reconstructing a vector from its components A x =3 A y =-4 1. Draw x and y axis x y 2. Go 4 units in positive x direction 3 3, Then go 3 units in negative y direction 4 4. Join origin to end point A θ