1. ## vector question2

given

vector U=(1,3,-2)
vector V=(-2,2,2)
vector W=(5,1,4)

demonstrate that vectors u,v, and w are all perpendicular to each other.

i took the dot product u dot v, v dot w, and u dot w and they all came to be 0.

is this complete after three dot products prove to be 0 demonstrating they are all perpendicular?

2. Your work is sufficient to prove the result, yes.

3. $\vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}| cos(\theta)$ where $\theta$ is the angle between them. If neither vector is the 0 vector and their dot product is 0 then we must have $cos(\theta)= 0$. Since $\theta$ must be between 0 and 180 degrees, that means $\theta$ must be 90 degrees- the two vectors are perpendicular.