how do i tell if a vector is parallel to another vector in $\Bbb R^6$?

Question

So far in my book I haven't learned any of the parallel or perpendicular notation.. so there must be some way to tell this answer that the book hasn't told me.. I looked back and there was nothing describing how to do it. How?

Answer 1

Others have already mentioned checking that one is a scalar multiple of another (and this is indeed the easiest way) but another possible method is to check if $$\mathbf{u}\boldsymbol{\cdot}\mathbf{v}=\Vert \mathbf{u}\Vert \Vert \mathbf{v} \Vert$$ If so, the vectors are parallel. If you're not working in $\mathbb{R}^n$, we can use $\langle \mathbf{u},\mathbf{v}\rangle$ instead.

Answer 2

Answers is $(b)$ and $(c)$ since we have $\textbf u= -\frac 12\textbf v$, where $v=(4,-2,0,-6,-10,-2)$, and $\textbf 0=0 \textbf u$.

It is worth it to mention that two vectors $\textbf u, \textbf v\in\mathbb R^3$ are parallel if the vector product $\textbf u \times \textbf v$ is equal to null vector $\textbf 0$.