Given unit vectors $\displaystyle q$ and $\displaystyle d_i$, i=1, 2, 3, ...,

$\displaystyle q, d_i \in \mathbb{R}^n

$

and we compute $\displaystyle q\cdot d_i$ and the L2 distance between them, $\displaystyle |q-d_i|^2=\sum_{j=1}^n (q_i-d_{ij})^2$, and we were to order the $\displaystyle d_i$'s in increasing order of those computations, show that the relative orders of $\displaystyle d_i$ would be the same for both cases (i.e. the inner product and L2-norm).

(This is paraphrased from a problem in a non-math book)

Any tips?