Vector Arithmetic

In this part we need to have a brief discussion of vector arithmetic.

Addition

We will begin with addition of two vectors. Thus, given the vectors a = a₁ , a₂ , a₃ and b = b₁ , b₂ , b₃ the addition of the two vectors is illustrated by the following formula.

 a^→ + b^→ = (a₁ + b₁ , a₂ + b₂ , a₃ + b₃)

The following diagram gives the geometric interpretation of the addition of two vectors.

This is occasionally known as the parallelogram law or triangle law.