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. 

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. 

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, question 1.

Draw a couple of arrows. For example, arrow PQ and arrow PR (it doesn't matter which pair of arrows you choose to draw with the three points). How do you know if two vectors are collinear?

Just a matter of using the appropriate formulas or relationships and setting up equations to solve for c.  I suggest you use the cosine of the angle between two vectors (could also use the sine formula). Note that cos(60)= 1/2.  Be careful! There is more than one answer for c.

Just a matter of using the appropriate formulas or relationships and setting up equations to solve for k.  What is necessary for two vectors to be parallel? orthogonal? same length?

A challenging question, but you may find Lesson 9, question 7 in my Lecture Problems of some help.

Part (a) is just a matter of following their instructions to generate the x-intercept Q and y-intercept R.

Part (b) is just telling you to make a graph with x-axis and y-axis, plot the points and draw the line through Q and R.

For part (d), note that the x, and y coefficients of the given line tell you the vector normal to the line.  Which is to say if given a line ax + by = c, then n = (a,b). 

Then, rather than do what I do in my question 7, you can find the distance they want in part (e) by computing the projection of arrow QP onto n.  The length of that projection vector is the distance you desire.

I strongly recommend  that you use the (x,y) graph to help.  You can then visualize the distance from P to the line by drawing a line from P perpendicular to the line.  Perhaps that will help you understand why the length of the projection vector gives you the distance in part (e).  Literally, you are projecting the arrow QP onto n, thus making a vector that is collinear with n but precisely the length you need, since that is the perpendicular distance from the point to the line.

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. 

The equation of the plane they gave you is irrelevant (that would only be needed if they had not given you the coordinates of the four vertices.  Note that you can confirm that the four vertices are on the given plane by verifying their coordinates satisfy the given equation.  For example, A(5,0,0) is on the plane 4x + 5y + 10z = 20 because 4(5)+5(0)+10(0) does indeed equal 20.

Note that the shape is not a parallelogram.  It is just a quadrilateral.  To find the area of any quadrilateral, cut along one of the diagonals to break it into two triangles and find the areas of those two triangles instead.  Then, it is just a matter of summing up those two areas.  See my Lesson 9, Practise Problem 28.