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
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.