How do I simplify the expression A - 4C + D when given polar vectors?

[DB]

i've posted this before, but i thought id start a new thread. before i go on ill let u guys know that this is not in my text, this is something my teacher wanted to throw in because he wants us to know it. I've been trying and trying and i just can't figure out wat to do.
4)given the following vectors in polar form: A = 10, 30 degress, B = 20, 225 degrees, C = 25, 340 degrees, D = 15, 110 degrees, simplify the following:
A - 4C + D
so i think wat I am supposed to do is convert the vectors to rectangular form, so here's wat i got:
all aproximations
A = [5, 8.7]
C = [23.5, -8.6]
D = [-5.1, 14.1]
so basically the only thing i thought of doing was this:
[5, 8.7] + 4[23.5, -8.6] - [-5.1, 14.1]
[5, 8.7] + [94, -34.4] - [-5.1, 14.1]
[5 + 94 + 5.1, 8.7 - 34.4 - 14.1]
[104.1, - 39.8]
i've never felt more wrong, n plus i still don't know wat to do with the angles, i wish i knew how do this but my teacher never did one with us so we are all on our own, in need of help, thanks...

 

[WalterContrata]

I think that you are on the right track. If asked to simplify the expression without further instructions, I would do as you have done. Please check your conversion to rectangular form, I think some of the coordinates are interchanged.

 

[WalterContrata]

...Strange that there is nothing to do with the vector B.

 

[DB]

lol no there is, that's just the first question, ill get to the other once i understand the concept
thnx for the reply btw
ive just looked them over i got the same answers, where do u think my mistake is?
and wat happens to the angles of the polar vectors?

 

[WalterContrata]

OK, how did you convert the polar coordinates to rectangular?

 

[DB]

i set the up on a cartisian plane, for example 25, 340 degrees would be a triangle in the 4th quadrant with the hypotneuse length 25 and the angle between the y-axis and the hypotneuse 70 degrees and then i used trig to solve the sides.

 

[Integral]

Just curious,

you computed

[5, 8.7] + 4[23.5, -8.6] - [-5.1, 14.1]

but the problem states A -4C+ D it looks to me like you computed A+4C - D.

 

[DB]

wow that's a stupid mistake, maybe that's wat walter caught. so then would the answer then be just: [-94.1, 57.2]? is that all?

 

[mathmike]

well no that answer is wrong you were closer with the first

i get 104.94,149.488

 

[DB]

maybe its kinda of against the rules here but can u show me how u did that?

 

[Integral]

You have made several small mistakes, but are very close. I would not dream of denying you the satisfaction of getting this right. I agree will all of your conversions to rectangular except for A, you have a rather obvious error, recompute that vector then do the correct arithmetic.

 

[DB]

thanks integral
sorry walter u were right about one of them being interchanged

so now that I've realized that A was reversed I am doing:
[8.7, 5]-[94, -34.3]+[-5.1, 14.1] to get: [-90.4, 53.5]

ionno if that's right because mike got a different answer...
btw whether its right or wrong can i write it like so: [-90.4i, 53.5j]?

 

[WalterContrata]

DB,
Good going. I got the same answer, except in the last sig. fig.'s.
As for how to write it, how does your teacher usually write these vectors? I often saw coordinates in brackets or parentheses like (3,4) or magnitudes with unit vectors, like 3i + 4j.

 

[DB]

he usually just writes it like this: [-90.4, 53.5], but as i was reading on the internet about vectors to help me with this problem i saw a lot of this: [-90.4i, 53.5j]

 

[WalterContrata]

If I were doing it, I would try to stay consistent with the teacher's style. That will minimize the probability of confusion in class. However, it is good to know there are other ways of writing these things, so that you can read textbooks with different notation, and pick a suitable style when you do your own problems.