The fractions (2/3), (4/6), (6/9), ... are all equivalent to the fraction (2/3). Explain how the concept of equivalent fractions is analogous to the concept of equivalent vectors.

Question

I completely lost, I don't know the answer or how to answer the question.

Answer 1

Frankly, I do not think it is all that analogous.
The point in vectors is that all vectors with the same length and direction are equivalent. It does not matter where they start , only their magnitude and direction.
So in x,y coordinates we might have a vector of length sqrt(2) and direction 45 degrees counterclockwise from the x axis (like north east)
You could say this was the vector from the origin (0,0) to the point (1,1)
HOWEVER
it is also the vector from (1,0) to (2,1)
and it is also the vector from (5,5) to (6,6)
In other words if they have the same length and compass heading, they are equivalent.
I have trouble comparing this to having common factors in the numerator and denominator, but that is all I can say.