Newbie Needs Help: Explaining Vectors, Scalars, and More!

[nike]

help the newbi please

I had a question about vectors and scalars. Can you explain it to me, and I also had a problem with this question.
here is the question:
Three vectors A,B, and c having magnitude of 50 units like in the x-y plane and makes angle of 30, 195,315 with positve x axis. find graphically and direction of the vectors.
A) a+b+c b) A-b+c

Can you guys also expalin the multipicaiton of vectors also please.

I also had another question what is C= absin, what is it use for?

Thanx guys, I'm a newbie here, and I was just wondering if you can suggest a basic physics book that I can use. thanks again.

 

[Knavish]

Can you show what you've done so far? Even if I disregarded the rules and helped you, I wouldn't know what to help you on. How much do you know about vectors?

 

[nike]

oh i didn't know about the rules lol. First i graphed the A,b,c, then I don't know what to do? If you can't tell me its ok. can give me an example of this problem how to do it. thanx. I also want to know about multipication of vectors too.

 

[matt grime]

first up, in general one cannot "multiply" vectors.

You have probably been given the "idiots guide to vectors" definition that they are things with direction and magnitiude. it is far simpler if you think of a vector as being "an ordered r-tuple of numbers". ok, may not sound it right now, but we just mean an array for example (x,y,z) {this is a 3 tuple} with r entries that are numbers. the "tuple" bit means that we consider the order of the entries important, that's all, and so we can consider the first, second, third etc entry. the most useful vectors to begin with are 3-tuples because we have three (spatial) dimensions to think about. the entries in the array (and lets' stick to arrays with 3 elements from now on) are called components and they will in the common physical interpretations (forces, displacement, etc) correspond to directions relative to some fixed frame of reference.

we can do several things with two vectors, and i think you are asking about the dot product of two vectors (also known as the inner product).

if we have a vector x=(a,b,c) we denote its length by |x| which is \sqrt{a^2+b^2+c^2}. given two vectors x=(a,b,c) and y=(p,q,r) then we set x.y=ap+bq+cr. this satisfies the relation that

x.y=|x||y|cos(t)

where t is the angle between the two vectors when we plot them in the stnadard xyz frame of reference.

If F is a force and d a displacement then the work done in the direction of d is F.d for instance.

i would suggest Arfken's mathematical methods.

vector addition can be visualized by thinking of these vectors as arrows if you like, or simply by noting that x+y=(a+p,b+q,c+r) ie you add components. the example you gave requires you to draw a picture, which i can't do here.

 

[Knavish]

Well, remember that the result of (A+B) added 'vectorially' to (C) is the same as (A+B+C). So, line up the vectors A and B head to tail, and add them. Then do the same thing with the result of that and C. If you don't know what I mean, just ask..

By "multiplication" I think you mean cross and dot product. AB(sin(theta)) is the cross product. This basically means to find the resulting vector that is perpendicular to both A and B. The math is just as it stands--the magnitude of A times B times sin of the angle inbetween gives the resulting magnitude. The resulting direction is found by using the right hand rule.

 

[nike]

hey matt, where did you get the Y from?
can you guys tell me what baisc physics book I can get?

 

[matt grime]

i told you what y was: another vector.