Question

Find the angle between the lines whose direction ratios are $3,2,-6$ and $1,2,2$.

Answer 1

$\left(l_1{m}_1{n}_1\right)=(3,2,-6)$ $\left(l_2{m}_2{n}_2\right)=(1,2,2)$

$\therefore \cos \theta =\frac{l_1{l}_2+m_1{m}_2+n_1{n}_2}{\sqrt{l_1^2+m_1^2+n_1^2}\sqrt{l_2^2+m_2^2+n_2^2}}$

$=\frac{3\times 1+2\times 2+(-6)\times 2}{\sqrt{3^2+2^2+6^2}\sqrt{1^2+2^2+2^2}}=\frac{-5}{21}$

$\therefore \theta ={\cos }^{-1}\frac{-5}{21}\Rightarrow \theta ={103.77}^0$