Did you read my tips on how to study and learn this course?  If not, here is a link to those important suggestions:

Did you miss my Tips for Assignment 1? Click here.

Did you miss my Tips for Assignment 2? Click here.

Here is a link to the actual assignment, in case you don't have it handy:

Study Lesson 9 (Vectors) and Lesson 10 (Lines and Planes) from my Linear Algebra & Vector Geometry book to prepare for this assignment.

Similar to my Lesson 9, question 1.  Note that, by the components of w, they are merely requesting that you state the vector w.  Be careful.  One of the parts cannot be done.

Pretty self-explanatory.  Once you have computed sinθ and cosθ, just sub the two answers into the identity in part (c) and simplify.  Obviously, you should end up getting 1.

Pretty much a combination of all my questions in Lesson 10.  Especially Lecture Problems 4, 7 and 10 and Pracise Problems 31 and 32.

Similar to my Lesson 10, question 6. 

This is just a matter of perseverance.  You must use letters, not numbers, to prove this is true for all R3 vectors.  For example, you could let u = (a,b,c), v = (d,e,f) and w = (g,h,i).  Then, just set to work computing the left hand side of the given inequality and the right hand side of the given inequality.  Lots of expanding and collecting like terms. 

For example, things like (a-g)^2 which must be expanded as (a-g)(a-g) = a^2 - 2ag + g^2.

You should discover that several of the terms are identical on both sides and can therefore be ignored.  Focus on what is different.

Similar to my Lesson 9, question 6. It is just kind of in reverse.  Since you are told these are R3 vectors, you could also use an approach similar to question 5 above.