MAB120 + MAB125 Problem Solving Task – C
Instructions
Due: 5.00 pm on Tuesday 29 May 2012
Submission procedure
Your assignment should be posted in the assignment box at the end of the corridor of level 6 in O-block
.
Do not use assignment minder!
Do not use a School of Mathematical Sciences Coversheet!
Do not use a folder or envelope when submitting your assignment!
You must restrict your submission to a single A4 piece of paper – preferably one side, preferably on photocopy
type paper.
Submission format
Your submission should be hand-written (you should keep a photocopy).
Include at the top of the page the following …
Family name, Given name Student number Workshop day, time, room
Questions – Vectors and Matrices
1.
A vector equation for a given straight line is r = (i + 3 j) + (i j).
(a)
Show that the point (1; 2) does not lie on this line.
(b)
Construct a vector equation for the line that does go through the point (1; 2), and is perpendicular
to r
.
(c)
Determine the point of intersection of the two lines.
2.
You have been assigned the task of breaking a recently intercepted coded message. The ecient running
1
of a battle requires secure communications. It has been discovered that the radio communications used
by the enemy has been coded. Just such a coded message has been intercepted and it reads as follows;
14; 10; 5; 9; 8; 14; 23; 35; 20; 13; 6; 5; 21; 8; 5; 5; 8; 5; 5; 1; 9 :
A chance nding in a document captured from the enemy reveals what you think may be the coding
matrix that generated this message.
Unfortunately you have two to choose from, namely
A =
2
4
1 2 1
2 1 1
1 3 0
3
5
; B =
2
4
1 1 1
2 0 1
1 0 0
3
5
:
Your task: Interrogation of some recent prisoners leads you to believe that one of the words in the coded
message you have been asked to decode refers to a bitter fruit. What is the entire message? You will nd
the additional notes on a simple coding exercise helpful here. [Hint: T=20]
Only if you are unable to physically comply with this request with good reason, then submit a .pdf le via email to
g.pettet@qut.edu.au where the attached le has the name \yourname studentnumber C.pdf”.
Semester one, 2012 nal corrected – May 24, 2012
1
SOLUTION
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1)(b) Since the line is perpendicular to the plane, the normal vector n, of the plane is also the directional vector of the line.
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