Activity 10.3 Application of Vectors
Overview:
The activity is a three-question worksheet that explores vectors. Question 1 involves
displacement, Question 2 asks students to determine if the result of certain vector operations,
and Question 3 illustrates a business application of vectors.
Estimated Time Required:
This activity should take approximately 30 minutes.
Technology: None
Prerequisite Concepts:
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The definition of displacement
Addition and subtraction of vectors
Scalar multiplication
Price and consumption vectors
Discussion:
This activity is designed to given students an introduction to some of the many uses of vectors.
An important new idea is that vectors are useful for organizing certain types of information.
1. Suppose you travel 3 miles West, then 4 miles Northwest. You then change
directions by 15 degrees more towards the North and travel 2 more miles.
a.) Sketch this scenario.
b.) How far are you from your starting point?
2. Is each of the following quantities a vector, a scalar, or undefined? Let
and let k be any nonzero scalar.
 v
a.) u  k
c.)
2
2u  3v
b.) u  v
2
d.)
u v
u and v be vectors,
3. A popular bagel shop sells several kinds of bagels. The four most popular varieties are onion,
chocolate chip, sunflower, and wheat, in that order. The selling price for all bagels is $0.50,
except for chocolate chip, which sells for $0.55. This can be represented by the price vector
P  0.50,0.55,0.50,0.50 . Due to different ingredients, each bagel costs a different
amount to produce. The expenses per vector can be displayed in the expense vector
E  0.32,0.38,0.29,0.27 . Let I be the inventory vector. If all the bagels are baked at
night, then at the start of the business day the shop has a certain number of each type of
bagel. Denote this vector by
I  I1 , I 2 , I3 , I 4 . Let C  C1 , C2 , C3 , C4 represent the
consumption vector. This vector gives the number of bagels of each type purchased each
day.
a.) Write a verbal description of the meaning of each of the following expressions or
equations:
i)
I C
ii)
C  0.8I  0
iii) P  E
b.) Write a mathematical expression that would give the following values:
i) The revenue for the day from the sale of the four types of bagels.
ii) The profit from the day from the sale of the four types of bagels.
iii) The maximum profit for the day from the sale of the four types of bagels.