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- Jul 26th 2010, 12:13 PMwiseguyVectors - help needed
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- Jul 26th 2010, 12:28 PMlvleph
a) You will need vector addition, which is just adding vectors componentwise.

b) Use the law of cosines

c) Use the formula where is the cross-product and is the magnitude.

d) Use the formula where is the dot-product.

If you don't understand those terms you will need to look them up. I believe your instructor intends for you to learn this on your own, so I won't be able to help you any further without an attempt at a solution. - Jul 26th 2010, 01:20 PMwiseguy
Is there a good page or something that defines this specific topic in vectors?

- Jul 26th 2010, 02:26 PMwiseguy
Is it as simple as adding the two equations together?

- Jul 26th 2010, 02:36 PMwiseguy
I attempted to solve as a system of equations with cramers rule with no success. :/

- Jul 26th 2010, 03:27 PMlvleph
You don't need Cramer's Rule. are called cardinal directions and represent components of a vector.

.

I would suggest using google or the search in the forums and look up the keywords I mentioned in my first post. - Jul 26th 2010, 03:59 PMwiseguy
Would you call this a difficult problem?

I'm taking my final tomorrow and I'm having no luck in getting a grasp on these vector problems :/ :/ I'd greatly appreciate this problem worked out, or explained, I have others on an assignment sheet I want to model it after. :) - Jul 26th 2010, 04:13 PMPlato
- Jul 26th 2010, 04:47 PMlvleph
The following is going to contain a very compressed version of what I would teach in about 1/4 to 1/2 a semester, so have fun.

**a)**We can write the vectors as

So adding them together we get

**b)**The law of cosines states where is the angle between . So to find the angle between two vectors we use the formula .

But, we need to discuss the dot product first. Say we have two vectors

then the dot product is defined as

.

Therefore, the dot product for our vectors would be

.

We also need to know how to find the magnitude of our vectors. The magnitude of a vector is given by

.

Therefore, we have

and so

.

Finally,

**c)**Here we need to discuss cross-products. In my opinion the easiest way to do a cross product is by using the cardinal directions.

First, draw a triangle with one of each at each vertex, in that order. Now draw arrows from each vertex going clockwise. This will help you remember the products that I am about to tell you

What we did there was start at the vertex crossed with the vertex, which then sends us to the vertex. Notice we went in a clockwise direction. If we traveled in the counter clockwise (anti-clockwise) direction we would have got a negative answer.

Here are a couple more examples

.

The next important thing is that

.

Now we can compute our cross-product

Now multiply these out similar to polynomials, except scalars multiply and vectors use cross-product. Also, in this case order of multiplication is important

The rest of this you should be able to do on your own.