Relation for angles between 3 unit vectors

35 Views Asked by At

Let there be $3$ unit vectors $\textbf{a}_1,\textbf{a}_2,\textbf{a}_3$ in $3\text{D}$. If we have $$\textbf{a}_1\cdot\textbf{a}_2=p$$ $$\textbf{a}_2\cdot\textbf{a}_3=q$$ $$\textbf{a}_1\cdot\textbf{a}_3=r$$ how do we find $p$ in terms of $q$ and $r$?