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Old Sep 27th 2009, 12:52 PM   #1
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Combining like terms?

This may come across as a rather silly question, but I'm having troubles combining like terms for a problem in physics (first year university level).

Please note:
ie. A(rightarrow) means a vector of A (A with the right arrow overtop)
ie. i(hat) is a unit vector i (with the hat overtop it)
ie. j(hat) is a unit vector j (with the hat overtop it)

The question:
1. Write each vector in terms of the unit vectors i(hat) and j(hat). Use the unit vectors to express the vector C(rightarrow) where C(rightarrow) = 3.00A(rightarrow) - 4.00B(rightarrow). Find the magnitude and direction of C(rightarrow).

My work so far:

2. Relevant equations
A(rightarrow) = Axi(hat) + Ayj(hat)
Ax = 3.60cos(70deg.)=1.23
Ay = 3.60sin(70deg.)=3.38
A(rightarrow) = 1.23i(hat) + 3.38j(hat)
B(rightarrow) = Bxi(hat) + Byj(hat)
Bx = -2.4cos(30deg.)=-2.078
By = -2.4sin(30deg.)=-1.2
B(rightarrow) = -2.078i(hat) + (-1.2)j(hat)

3. The attempt at a solution
C(rightarrow) = 3.00A(rightarrow) - 4.00B(rightarrow)
C(rightarrow) = 3.00(1.23i(hat) + 3.38j(hat)) - 4.00(-2.0781i(hat) + (-1.2)j(hat))
C(rightarrow) = (3.69i(hat) + 10.14j(hat)) - (-8.312i(hat) + (-4.8)j(hat))

I got stuck at this stage; I'm pretty sure up until now I've been doing it right, but now I'm a little confused about combining the like terms (ie. ihat with ihat and jhat with jhat terms). Would I, for instance with the jhat terms, go 10.14-(-4.8) which would give me a large positive number? or would I just go 10.14(-4.8) which equals 5.34, and then subtract it later (ie. -4.622i(hat) - 5.34j(hat))?

Basically, I just need to know what to do from here. I'm pretty sure I know how to solve for the magnitude and direction once I figure out these terms.

Note: A similar, simpler question to this one would be how to combine the like terms for this one:

A(rightarrow) - B(rightarrow)
(4.00i(hat) + 3.00j(hat)) - (5.00i(hat)+(-2.00)j(hat))

Would the answer for that one be 9.00i(hat) - 1.00j(hat)?

I know it's simple algebra but for some reason it's evading me =\

Thanks for any help!

Last edited by dark-ryder341; Sep 27th 2009 at 12:55 PM.
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Old Sep 29th 2009, 04:36 AM   #2
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One request please. Could you rewrite this using boldface i j k for the unit vectors and A etc. for vectors?

Hats off to you for writing it like this, but im kind of getting lost in them, so get the hats off the unit vectors!
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