Exercise 20

We can give a justification for the convention that the sum of zero-many vectors equals the zero vector. Consider this sum of three vectors $\vec{v}_{1}+\vec{v}_{2}+\vec{v}_{3}$.

• What is the difference between this sum of three vectors and the sum of the first two of these three?

• What is the difference between the prior sum and the sum of just the first one vector?

• What should be the difference between the prior sum of one vector and the sum of no vectors?

• So what should be the definition of the sum of no vectors?