Vector Components and Coordinates: Finding Vectors in Terms of Coordinates and Angles, Slides of Physics

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Vector Components

Coordinates 

Vectors can be described in terms of coordinates.

-^

6.0 km east and 3.4 km south

-^

1 N forward, 2 N left, 2 N up



Coordinates are associated with axes in a graph.

y

x

x^

= 6.0 m

y^

= -3.4 m

Ordered Set 

The value of the vector ineach coordinate can begrouped as a set.



Each element of the setcorresponds to onecoordinate.

-^

2-dimensional

-^

3-dimensional



The elements, called components

, are scalars, not

vectors.

A

A

A

A

y

x

v

v

v

v

v

z

y

x

Component Addition 

A vector equation is actuallya set of equations.

-^

One equation for eachcomponent

-^

Components can be addedlike the vectors themselves

N

N

N

N

N

N

N

N

y

x

y

y

y

x

x

x

y

x

y

x

C

C

C

B

A

C

B

A

C

B

A

C

B

B

B

A

A

A^ 

Vector Direction 

Vector components can also be used to determinethe direction of a vector.



The tangent of the angle from the

x

-axis is the ratio of

the

y

-component divided by the

x

-component.

y x

A A



tan

4.1 N

2.1 N

4.6 N^ 

Components to Angles 

Find the magnitude andangle of a vector withcomponents

x

= -5.0 N, y =

3.3 N.

y

x

x^

= -5.0 N

y^

= 3.3 N^ 

= 33

o^

above the

negative

x

-axis

L

tan

tan

1

2

2

2

2

2

x x y

y

y

x

L

y

x

L









L

= 6.0 N