Vectors

Force Position Velocity

Vector quantity

In order to be completely spcified we need to know its MAGNITUDE and DIRECTION

Scalar quantity

AirplaneRabbit

v

g

X

Z

1D

1D

x v

v

y

X

Y

vector position

2D

Finding the vector components (with respect to a particular reference) Example

Example

Page 7

AzMagnitude of A = |A| � [ (Ax )2 + (Ay )2 + (Az )2 ]1/2

Unit Vector

That is,

Addition of Vectors By combining their axis components

Addition of Vectors Tail-to-tip graphic method

Example The same vector c expressed in different ways

Example

Page 16 EXAMPLE

j

i

u

45oF

F = 20 Kg-f

Unit of force

u = ?

Express the vector F in terms of the unit vectors and .

Find the unit vector whose direction is parallel to the ramp.

i j

=

Multiplication of Vectors

Scalar product

Geometrical interpretation of the scalar product

= +

+

-

The Vector Product

Z

X