Question

Find angle in degrees between the line joining the points $(2,1,3)$ and $(1,-1,2)$ and the line having direction ratios $2,1,-1$.

Answer 1

Direction ratio of line passing through the points (2,1,3) and (1,-1,2)

are $2-1,1-(-1),3-2=1,2,1$

Let angle between them be $\theta$

Now, $\cos \theta =\frac{2\times 1+1\times 2+1\times -1}{\sqrt{1^2+2^2+1^2}\sqrt{2^2+1^2+(-1{)}^2}}=\frac{3}{6}=\frac{1}{2}\Rightarrow \theta =co{s}^{-1}\frac{1}{2}\Rightarrow \theta ={60}^o$