Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Preliminary Questions - Page 666: 3

Distributive property.

If $ v $ is orthogonal to $ u $ and $ w $, then we have $$ v\cdot u=0, \quad v\cdot w=0.$$ Now, $ v\cdot (u+w)=v\cdot u+v\cdot w=0$, which means that $ v $ is orthogonal to $ u+w $. Hence, we use the distributive property.