A street vendor

  • Thread starter Calpalned
  • Start date
  • #1

Homework Statement

A street vendor sells a hamburgers, b hot dogs, and c soft drinks on a given day. He charges $2 for a hamburger, $1.50 for a hot dog, and $1 for a soft drink. If A = <a, b, c>, and P = <2, 1.5, 1> , what is the meaning of the dot product A * P

Homework Equations

- Dot product of <x, y, z> and <a, b, c> is xa + yb + zc
- Two vectors multiply to become a scalar.

The Attempt at a Solution

I have no clue what the significance of the dot product in this situation is. Additionally, I don't see how $1.50 and nor the number of hot dogs are vectors.

Answers and Replies

  • #2
Imagine they didn't say anything about vectors and just gave you the equation "2*a + 1.5*b + 1*c", would you know what it describes? You're multiplying the price of something by the number of those things you sold. What does that mean in real life?

As for the vectors:

Without all this business about hotdogs and money, do you know how to interpret <1, 2, 3>? It means that x = 1, y = 2, z = 3 in a traditional Euclidean space, right?

Now just imagine that instead of x, y, z we relabel them "x = number of hamburgers, y = number of hotdogs and z = number of soft drinks". In this case x = a, y = b, z = c so they form a vector <a, b, c>.

Do the same thing for the price. "x = price of a hamburger, y = price of a hotdog, z = price of a drink" then our vector is <2. 1.5, 1>.

Doing the dot product we get 2*a + 1.5*b + 1*c

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