Direction cosines

Question

I have two vectors, $\vec A$ and $\vec B$ that meet at point R. The vector $\vec {RA}$ has a magnitude 2km and direction cosines $\cos(\alpha)$=0.768, $\cos(\beta)$=0.384, $\cos(\gamma)$=0.512. The vector $\vec {RB}$ has a magnitude 4km and direction cosines $\cos(\alpha)$=0.743, $\cos(\beta)=0.557$, $\cos(\gamma)=-0.371$. What is the angle theta between the vectors $\vec {RA}$ and $\vec {RB}$?

Answer 1

You know that $\displaystyle\cos\theta=\frac{u\cdot v}{|u||v|}$, where

$u=RA=2(.768,.384,.512)$ and $v=RB=4(.743,.557, -.371)$;

so $\theta=\cos^{-1}[(.768)(.743)+(.384)(.557)-(.512)(.371)]$.