1. 3 Vectors in Physics 3-1 Scalars versus Vectors
Scalar: a number with unit
volume, time, temperature, distance …
Vector: a mathematical quantity with both direction and magnitude
velocity, acceleration, displacement …

2. Vector: draw diagram or sketch Magnitude: length of line
Direction: arrow
(2) Vector: write
Boldface, r
Draw arrow over the vector’s symbol
Magnitude: r=|r|=| | θ x y r

3. 3-2 The component of vector
Resolve or decompose vector on the x and y axis θ x y r rx ry θ
Hypotenuse (H)
Opposite (O)
Adjacent (A)

4. II
x -, y+
sin +, cos -, tan -
900<ϴ<1800
I Quadrant
x +, y+
sin +, cos +, tan +
0<ϴ<900
1800 -α α
III
x -, y-
sin -, cos -, tan +
1800<ϴ<2700 IV
x +, y -
sin -, cos +, tan -
2700<ϴ<3600
1800 +α
3600 –α or -α

5. Ex1.
O=?, H=?
O=? 2
300
400 3 A O
O=?, A=?
θ=?, O=?
Θ=? 2 1

6. Ex2.
Say you walk 3 m right and 11 m north, find the magnitude and direction of displacement.
Ex3 θ O x y
-2m
-1 m
r=?, θ=?

7. 3-2 Adding and Subtracting Vectors
Adding vectors Graphically
Connect vector head and tail, the sum vector is free tail to point free head C D B C B A A

8. Adding Vectors: parallelogram method
Adding Vectors Using Component
Cx=Ax+Bx
Cy=Ay+By
Ex1.
A=3, ; B=5, C=? A C B

9. Ex2. C=? Ex3. A=2 m, θ=250; B=3 m, θ=600 Find | | and θ Ex4.
300
600 2 3
Ex2.
C=?
Ex3.
A=2 m, θ=250; B=3 m, θ=600
Find | | and θ
Ex4.
A= 3 m, θ=600, B=5 m , θ=
600
1600
200 A B

10. Subtracting Vectors Dx=Ax-Bx Dy=Ax-By Ex4. A= 10 m, 300; B=5 m, 600
Find , magnitude and direction ?