Physics Presentation

Members of the Group ,[object Object],[object Object],[object Object],[object Object]

Scalars Vectors ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Why vectors are important? ,[object Object]

Properties of a Vector ,[object Object],[object Object],[object Object],O A |A| ≡ A

Types of Vector ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Laws of vector algebra ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Addition of Vectors ,[object Object],[object Object]

Methods of Addition of Vectors ,[object Object],[object Object],[object Object],[object Object],[object Object]

Parallelogram law ,[object Object],[object Object],[object Object],P Q + P P Q Q +

Triangle law (head to tail rule) ,[object Object],[object Object],[object Object],P Q + P Q P Q +

Subtraction of vectors ,[object Object],[object Object],[object Object],P Q - P -Q P-Q P P -Q -Q = OR

Resolution of a vector ,[object Object],[object Object],[object Object]

Resolution of a vector ,[object Object],[object Object],R 0 Rcos0 Rsin0 R  Rcos  Rsin 

Triangle of forces ,[object Object],[object Object],[object Object]

Triangle of forces ,[object Object],o P Q R A C O R P Q P+Q A C O P R Q

Polygon of Forces ,[object Object]

Polygon of Forces ,[object Object],o S T P Q R Q R S P T A B C D E

Resultant of a number of forces ,[object Object],[object Object],A B C D E A B C D E R o

[object Object],[object Object],[object Object],PRODUCT OF VECTORS M.Adil Bashir

Scalar product or Euclidean inner product ,[object Object]

WHY SCALAR PRODUCT IS USE ,[object Object],[object Object],A . B = A B COS θ

SPECIAL CASES ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],X Y X X Y Y

SCALAR PRODUCT ,[object Object],The Dot Product of a vector with itself is always equal to its magnitude squared ,[object Object],[object Object],When A and B are parallel to each other, their Dot Product is identical to the ordinary multiplication of their sizes When A and B are perpendicular to each other, their Dot Product is always Zero

SCALAR PRODUCT ,[object Object],[object Object]

SCALAR PRODUCT IN COMPONENT FORM ,[object Object],[object Object],[object Object],[object Object]

LAWS OF DOT PRODUCT ,[object Object],[object Object],[object Object],[object Object],B BCOS θ A B ACOS θ A B A R=A+B C

EXAMPLES OF SCALAR PRODUCT ,[object Object],[object Object],[object Object],[object Object]

EXAMPLES OF SCALAR PRODUCT ,[object Object],[object Object],P = F . V ,[object Object],[object Object],Electric flux = E . A

EXAMPLES OF SCALAR PRODUCT A reader has used the dot product to help him analyze the movements of a tagged right whale. He had the x and y coordinates for a set of positions of the whale and wanted to calculate the angles turned through between successive sections of its journey. He found each section as a vector by calculating the differences between the pairs of x and y coordinates of the endpoints. Then he used the dot product of each successive pair of vectors to find the angle between those two legs of the whale's journey. A right whale fluke © the New England Aquarium

CROSS PRODUCT Q.What is Cross Product ? Hassaan Ahmed Usmani

What is Cross Product ,[object Object],[object Object]

Cross Product ,[object Object],[object Object],[object Object]

The right hand rule ,[object Object]

Cross Product of standard basic vectors

Geometric Meaning ,[object Object]

Examples of cross product ,[object Object],[object Object]

Examples of cross product ,[object Object],[object Object],[object Object]

Torque ,[object Object],[object Object]

POINT,LINE AND PLANE By Naeem Nassiruddin

What is Line? ,[object Object],[object Object],[object Object],A B

Line ,[object Object],[object Object],R T S U V

Line ,[object Object],[object Object]

Skew Line ,[object Object],[object Object]

Postulates of Geometry ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Q P T l m A B C

[object Object],[object Object],M N D E

What is Plane? ,[object Object],[object Object],[object Object],B A C

Quadrants of Plane y x 5 -4 -2 1 3 5 5 -4 -2 1 3 5 -5 -1 4 -5 -1 4 -3 -5 2 2 -5 -3 Quadrant I (+, +) Quadrant II ( – , +) Quadrant III ( – , – ) Quadrant IV ( + , – )

Equation of plane in 3D This time, the locus is a plane .

Thank You !! Any Questions??????

Physics Presentation

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