Don't have my book or audio lectures?  You can download a free sample of my book and audio lectures containing Lessons 1, 2 and 9:

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.

Besides thoroughly studying Lesson 9 in my book, Lesson 9, question 6 is similar, and you may find questions 29, 30 and 31 in my Practise Problems for that lesson helpful in understanding the kind of things to do for this question.

Hint: How does arrow OB relate to arrow OA?

Use a dot product and the results you found in part (a), similar to my question 6.

Similar to my Lesson 9, question 1.

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

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).

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 triangle.  See my Lesson 9, Practise Problem 28.