Component of vector a along the direction of b
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Component of vector A along the direction of B. A. Project A onto B: Drop perpendiculars to B. This component is positive. B. A. This component is negative. B. Sometimes only one perpendicular needs be dropped:. A. B. Weight of object on an incline. Choose B to point down incline. B.

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Component of vector a along the direction of b l.jpg

Component of vector A along the direction of B

A

Project A onto B:

Drop perpendiculars to B

This component is positive

B

A

This component is negative

B


Sometimes only one perpendicular needs be dropped l.jpg
Sometimes only one perpendicular needs be dropped:

A

B

Weight of object on an incline

Choose B to point down incline

B

A


Special cases l.jpg
Special Cases

A

5

Component = +5

B

5

B

A

Component = -3

3

3

A

Component = 0

B



How to calculate components l.jpg
How to calculate components

A

1. Make component part of a triangle containing A

5

2. Identify an angle in the triangle

x

3. Use trig to find length of component: sine or cosine?

Adjacent. Therefore cosine.

Length of component =5cos30°=5×0.866=4.33

4. Add appropriate sign:

X-Component = - 4.33


How to calculate components7 l.jpg
How to calculate components

A

1. Make component part of a triangle containing A

5

2. Identify an angle in the triangle

5

x

3. Use trig to find length of component: sine or cosine?

Opposite. Therefore sine.

Length of component =5sin60°=5×0.866=4.33

4. Add appropriate sign:

X-Component = - 4.33


Component of sum sum pf components l.jpg
Component of sum=sum pf components

y

Cx=Ax+Bx

B

C=A+B

A

Cy=Ay+By

x

Cx

Bx

Ax


Reconstructing a vector from its components l.jpg
Reconstructing a vector from its components

y

Ay=-4

Ax=3

1. Draw x and y axis

2. Go 4 units in positive

x direction

3

x

θ

3, Then go 3 units in

negative y direction

4

A

4. Join origin to end point


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