Question

Find the angle between the two lines whose direction cosines are:

2/3,-1/3,-2/3 and 3/7,2/7,6/7

Answer 1

Let 

R₁ = \(\frac{2}{3}i\) - \(\frac{1}{3}\)j - \(\frac{2}{3}\)k

and R₂ =  \(\frac{3}{7}i\) + \(\frac{2}{7}\)j + \(\frac{6}{7}\)k

R₁.R₂ =  |R₁||R₂|cosθ

Here, as R₁ and R₂ are the unit vectors with a direction given by the direction cosines hence, |R₁| and |R₂| are 1.