Chapter 3Vectors in Physics

Dr. Haykel Abdelhamid Elabidi

1st/4th week of October 2013/DhH 1434

Units of Chapter 3

• Scalars versus vectors

• The components of a vector

• Adding and subtracting vectors

• Scalar product or dot product

• Vector product or cross product

Scalars versus VectorsA scalar is a number with units. It can be positive, negative or zero.

Scalar quantitiesMasse

Temperature

Energy

Power

Speed

Vector quantitiesVelocity

Acceleration

Displacement

Force

Field

A vector is a mathematical quantity with both a magnitude and a direction

Your home

School?

To describe where the shool is located versus your home, It is not sufficient to give the distance between them. we have to give the distance and the direction.

School?

School?

2 km

2 km

2 km

The components of a vectorA vector in xy plane can be resolved in two components.

The components of a vector

The components of a vectorExersise 3-2 page 61:

A

A vector is defined by its magnitude and direction, regardless of its location

The components of a vector

Adding and subtracting vectorsAdding Vectors Using Components:

1. Find the components of each vector to be added.

2. Add the x- and y-components separately.

3. Find the resultant vector.

ABBAC

Adding and subtracting vectors

Subtracting Vectors: The negative of a vector is a vector of the same magnitude pointing in the opposite direction. Here D= A B

BABAD

Example:Adding and subtracting vectors

Adding and subtracting vectors

Multiplying vector by 3 increase its magnitude by a factor of 3, but does not change its direction. If it is multiplied by -3, its magnitude is increases by 3 but it will has the opposite direction.

Multiplying vector by scalar

The result of the scalar product of two vectors and is a scalar:

Scalar product or dot product

A

B

Scalar product or dot product

The result of the vector product of two vectors and is a vector that is perpendicular to the plan of the two vectors:

Vector product or cross product

A

B

Thank you for your attention

See you next time Inchallah