Did you read my tips on how to study and learn Math 1300?  If not, here is a link to those important suggestions:

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

Note that you need to study Lesson 1 (Systems of Linear Equations) and Lesson 9 (Vectors) from my Linear Algebra & Vector Geometry book to prepare for this assignment.  I think you should find this assignment fairly straightforward if you do thoroughly study and do all the Practise Problems I give you in Lesson 9.  However, make sure that you study Lesson 1 of my book first.  It is an important review of key skills you will need throughout the course and assignments.

Do note that my free sample above does include my audio lectures for both Lessons 1 and 9.

Thoroughly study Lesson 9 in my book.  Lesson 9, question 6 is similar, and you may find Practise Problems 25 to 31 (especially 29) in my lesson very helpful in understanding the kind of things to do for this and all the questions in this assignment. 

Hint: What is the relationship between arrow OA and arrow OB?  Do note that OA, OB, and OC are all radii, so their arrows have the same length.

Part (b) is a matter of proving the two arrows you were given in part (a) are orthogonal. How do we know if two vectors are orthogonal?

Similar to my Lesson 9, questions 2 and 4.

Find arrow AD (or DA) in terms of k and arrow BD (or DB) in terms of k.  Find the lengths of those arrows in terms of k and set the lengths equal to solve k.  Be careful!  There is more than one answer.

Similar to my Lesson 9, question 1.

Anytime angles are mentioned, consider the formulas for the cosine or sine of an angle between two vectors.  Which one do you think would be better here?  Note my quick trig review on pages 298 and 299 of my book.

Understand that the picture they have drawn is in three dimensions.  Visualize the x-axis running west-east on your page, the y-axis running north-south, and the z-axis rising up like a pole from your table top. 

Again, this problem is just an application of the cosine formula.  You will need the three vectors in the direction of the x-, y-, and z-axes. 

Note, on any given axis, the other two coordinates are 0.  For example, on the x-axis, both y and z are 0.  So, the easiest vector to use in the direction of the x-axis is (1,0,0).  You could use anything in the form (k,0,0) as long as k is not 0.  Thus, alpha is the angle between the given vector (2,3,4) and the vector (1,0,0). 

Understand that the picture they have drawn is in three dimensions.  Visualize the x-axis running west-east on your page, the y-axis running north-south, and the z-axis rising up like a pole from your table top. 

Hint:  Draw a diagonal through this quadrilateral to make two triangles.  Add the area of the two triangles together.  See my Practice Problem 28.