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3. two vectors are defined as p2ij and q0ija robot starts...

# Question: two vectors are defined as p2ij and q0ija robot starts...

###### Question details

Two vectors are defined as p=2i+J and q=0i+j

A robot starts from the origin and moves using the vectors p and q.

The robot can use the vectors singly, reversed, combined or in multiples of each vector.

a) Find the end coordinates of three different robot moves.

p+q = (2i, 2j)
p-q = (2i, 0j)
q-p = (-2i, 0j)

b) By observing the pattern of your solutions to part a, show that a general algebraic solution for the end-point coordinates of any combination of vectors p and q is (2h,k) where h and k are integers
Give an example to show that this rule is true. (Hint: consider p - q).