The Smith's have arrived at the local supermarket, Watmart, on a lovely Sunday morning.

    Zack: "Mummy, can I help pick up food today?"

       Mom: "Sure!  What would you like to collect?"

   Zack: "Candy!"

   Dad: "I don’t think we need too much candy!  How about you collect the fruits?  There will be a lot of picking and putting into bags, and you can practice the counting you learnt in Math class.  What do you think?"

    Mom: "That sounds exciting!  We can meet up at the cash registers once we are done!"

Zack meets Bruno

Zack arrives at the apple stand.

Bruno: "To get around this grid (the supermarket), I will give you numbers in a box, called vectors, presented by square brackets.  If the number has a plus before it, means we move East or North, and a number with a minus before it, means we move West or South.  Depending on how the numbers are aligned in the box, we can figure out where to go.  The first number in the box always points right (East) or left (West), and the second number always points up (North) or down (South)."

Bruno describes to Zack how going 2 steps South and 7 steps East is one direction vector added together (draw grid layout from the apple stand to the banana stand).

Bruno: "Here is your first box, 

                          [-2, +5], 

the direction vector to the apple stand.  What does the first number tell us?"

Zack: "To take 2 steps left, because of the minus, and it is the first number."

Bruno: "Great!  And the second number?"

Zack: "5 steps North, because it is positive and the second number."

Bruno: "Great!  Let's go to the apple stand."

Zack understands the operation and Bruno provides Zack his third direction vector to the orange stand.

Bruno: "Zack, did you see how we first moved 2 steps left, and then moved 5 steps up?"

Zack: "Yes!"

Bruno: "I could have given you two boxes separately and said to add these two vectors to get a final vector.  Let me make myself clearer:

Lets say I gave you two vectors [-2, 0] and [0, 5].  Do you see if I added the left numbers together and the right numbers together, from each box, I would get [-2, 5]?"

Zack: "Sooo, you basically added the numbers in the vectors to get one vector.  That’s like addition they taught us in school.  5 apples + 2 apples gives 7 apples."

Bruno: "Exactly!  Here is your next vector [+7 -2], to the banana stand.  Can you figure out what it means?"

Zack: "Okay, plus 7 means we go 7 steps to the East, then I see minus two, so two steps South?"

Bruno: "Perfect! Let’s go get some bananas!"

Zack arrives at the orange stand.

Zack puts 5 oranges in his bag.

Bruno: "How do you think we could separate this into two vectors added together?"

Zack: "Well, we first went 7 steps East, so    [7, 0].  Then we went 2 steps South, so      [0, -2].  Sooo, [7, 0] +[0, -2] = [7, -2]!  This is getting easier!"

Bruno: "That is great!  Here is the next vector to my favourite fruit, oranges!

                   [+7 ,+2]"

Okay! Now I understand how direction vectors are helping me reach different stands. So I was at the banana stand and I travelled 2 steps North and 7 steps East to reach the orange stand!