Physics Quantities Vector Quanties Scalar Quantities Consist of

What is the Vector Quantities and scalar Quantities ? Vector QuantitiesScalar Quantities Have a magnitude and direction Have a magnitude without direction Example Velocity, Acceleration, Force Example Mass, Volum, Time,temperature

About Notation Vector Quantities Scalar Quantities A or A A Ex : r, v, F r, v, F Ex :m,T,L

Representation of vector Direction of line Length of line expressed by magnitude Tail Head A

Direction of Vector A -A B -B C -C Note : Direction of vector A,B changes since it is negative

Resultan is the total of two or more vector How the resultan in the same direction? 10 km 20 km

How the resultant in opposite direction? 5 cm 10 cm 5 cm A B R So, the resultan

Addition & Subtraction of vector A + B = R A – B = A + (-B)

The Addition & Subtraction can be Performade by Geometrical Methode Analytical Method Polygon Method Parrallelo gram Method Cossinus Method Component Method

A B R=A+B Polygon method

A B R=A+B Parallelogram method

How the describe in three vector A BC AB C R= A – B+C

Use the triangle and parallelogram methods to describe the result 5 cm 3 cm 4 cm a)A + B + Cd)A- B – C b)A + B - Ce)A – B + C c)(A – B ) + C

Analytical Method Cossinus Component A ά β R B Two Dimension Three Dimension BARif 

Component Method V x =V cos α,V y = Vsinα V = Vxi + Vyj Vx Vy V X Y α

Example 1.A vector velocity (v) form an angle 30 0 with positive x axis and the magnitude is 20 m/s. Determine the magnitude of vector components? 2.Two vector s of velocity have base point which coincide,those are v 1 =3m/s and v 2 =4m/s, ά=60 0,find the magnitude and direction of vector resultant

solution Known : v=20 m/s, =30 0 Asked:v x and v y Answered: v x =v 0 cos άv y =v 0 sinα v x =20 cos 30v y =20sin30 =20.1/2 =10 m/s

2. v 1 =3m/s,v 2 =4 m/s, ά=60 0 v= V= Cos 60 0 V = 37

i j x y Three dimensional i=j=k=1 units z k

x y z A AiAi AkAk AjAj A = A x i+A y j+A z k A= A + B= (A x +B y )i+(A y +B y )j+(A z +B z )k A – B = (A x -B y )i+(A x -B y )j+(A z +B y )k

Vector Multiplication 1.Dot Product Vector 2.Cros Product Vector A. B = AB cosα Dot Product vector gives a scalar unuts Ex: W=F.s A x B = C=AB sin α Cross product gives a new vector result

Polygon Method + = A B R=A + B A B Parrallelogram + = A B A B R=A+B