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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.
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.
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.