Math 1300 Distance: ICYMI Tips for Assignment 1

Published: Mon, 09/22/14

Did you read my tips on how to study and learn Math 1300?  If not, here is a link to those important suggestions:
Tips for Assignment 1
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.

Don't have my book?  You can download a free sample of my book and audio lectures containing Lessons 1, 2 and 9:
Question 1
Thoroughly study Lesson 9 in my book.  Lesson 9, question 6 is similar, and you may find Practise Problems 25 to 31 in my lesson very helpful in understanding the kind of things to do for this and all the questions in this assignment.
Question 2
Standard stuff.  Similar to my Lesson 9, question 4.

For part (b), try C = (a, b, c) and then set up equations to solve for a, b and c.

You will need your formula for the length of a vector to solve part (c).
Question 3
Similar to my Lesson 9, question 1.
Question 4
More of the same.  Very similar questions in my Practise Problems.
Question 5
A challenging question, but you may find Lesson 9, question 7 in my Lecture Problems of some help.

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.
Question 6
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 three points they want are the x-, y- and z-intercepts.  To get an intercept, simply make the other two coordinates 0.  For example, the x-intercept is where y=0 and z=0.  Sub that into the given equation to get the coordinates of the point. Make sure you are labelling correctly which one is A, B and C.