Combining like terms in a physics problem

[dark-ryder341]

This is for a first year university question in Physics (Mechanics).


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

Homework Equations

A[tex]\rightarrow[/tex] = Axi(hat) + Ayj(hat)
Ax = 3.60cos(70deg.)=1.23
Ay = 3.60sin(70deg.)=3.38
A[tex]\rightarrow[/tex] = 1.23i(hat) + 3.38j(hat)

B[tex]\rightarrow[/tex] = Bxi(hat) + Byj(hat)
Bx = -2.4cos(30deg.)=-2.078
By = -2.4sin(30deg.)=-1.2
B[tex]\rightarrow[/tex] = -2.078i(hat) + (-1.2)j(hat)

The Attempt at a Solution

C[tex]\rightarrow[/tex] = 3.00A[tex]\rightarrow[/tex] - 4.00B[tex]\rightarrow[/tex]
C[tex]\rightarrow[/tex] = 3.00(1.23i(hat) + 3.38j(hat)) - 4.00(-2.0781i(hat) + (-1.2)j(hat))
C[tex]\rightarrow[/tex] = (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. Thanks very much for any help!

 

[kuruman]

Hi dark-ryder341, welcome to PF.

We can't help you and check your work unless you state the problem. You have only stated the question but you did not provide the given quantities. "Write each vector" implies that there are given vectors which you have but we don't. Is there a picture that goes with this?

 

[dark-ryder341]

Yes, sorry, there is a picture that goes with this:

That's it right there.

Thanks for any help :)

 

[kuruman]

The i-hats and j-hats add just like apples and oranges. You add all the i-hats together and then separately you add all the j-hats together. That's why we use the "hats", to keep the components separate. So your first idea is correct. The j-hat component of C is 10.14-(-4.8).