Consider 3 unit vectors ${\bf a}$, ${\bf b}$ and ${\bf c}$. We know that ${\bf a}\cdot {\bf b}=0$ and ${\bf a}\cdot {\bf c}=1$. Can we say something about ${\bf b}\cdot {\bf c}$?
Also, when dealing with this problem can we consider WLOG that one of the vectors (e.g., ${\bf a}$) is $[1~~ 0~~ 0~ \cdots ~0]$?
If they're unit vectors, then $\mathbf{a}\cdot \mathbf{c}=1\implies \mathbf{a}=\mathbf{c}$, so $\mathbf{b}\cdot\mathbf{c}=\mathbf{b}\cdot\mathbf{a}=0$