Subtracting this vector - as opposed to adding it

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    Subtracting Vector
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To find the vector difference D = A - B, the components of vector B must be negated, resulting in -B. The correct calculations involve using the angle of B in the appropriate quadrant, which can lead to confusion. The x and y components of -B should be calculated as -Bcosθ and -Bsinθ, respectively. The final values for the resultant vector R and angle θ must be checked to ensure they are in the correct quadrant, as incorrect quadrant placement can lead to errors in the solution. Understanding vector subtraction is crucial for accurately sketching the vector difference.
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Homework Statement


Sketch the vector difference D = A - B

I have found F = A + B.

Homework Equations



A(x) = AcosTHETA
A(y) = AsinTHETA
B(x) = BcosTHETA
A(y) = BsinTHETA

R = sqrt(rx^2 + ry^2)

The Attempt at a Solution



As opposed to the F = A + B I have tried changing the signs of B or multiplying B(x) = -BcosTHETA etcetera and I can't come with the right solution. Do I need to put the angle 37 degrees in the second quadrant? I am confused as how to find -B as A is going to be the same as the first equation (F = A + B).
 

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rpgnick85 said:

Homework Statement


Sketch the vector difference D = A - B

I have found F = A + B.

Homework Equations



A(x) = AcosTHETA
A(y) = AsinTHETA
B(x) = BcosTHETA
B(y) = BsinTHETA

R = sqrt(rx^2 + ry^2)

The Attempt at a Solution



As opposed to the F = A + B I have tried changing the signs of B or multiplying B(x) = -BcosTHETA etcetera and I can't come with the right solution. Do I need to put the angle 37 degrees in the second quadrant? I am confused as how to find -B as A is going to be the same as the first equation (F = A + B).
attachment.php?attachmentid=43021&d=1327282200.jpg

Hello rpgnick85. Welcome to PF !

You would have
-Bx = -Bcosθ

-By = -Bsinθ​
That puts -B in the third Quadrant, doesn't it?
 
-Bx = -Bcosθ

-By = -Bsinθ

Does that mean that I would do -18cos(217) for my first value?
 
rpgnick85 said:
-Bx = -Bcosθ

-By = -Bsinθ

Does that mean that I would do -18cos(217) for my first value?
No.

The x component of -B is either 18cos(217°) or -18cos(37°) .
 
alright so when i use -18cos37 and -18sin37 for my Bx and By values respectively and 12cos180 and 12sin180 for my Ax an Ay values I am coming up with R= 28.5126 and θ=22.33° which is incorrect
 
found the answer- was in the wrong quadrant
 
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