Mathematics - Vector Question with Solution | TestHub

If $\left(l_1,m_1,n_1\right)$ and $\left(l_2,m_2,n_2\right)$ are the direction ratios then angle between the lines is $\cos \theta =\frac{l_1{l}_2+m_1{m}_2+n_1{n}_2}{\sqrt{l_1^2+m_1^2+n_1^2}\sqrt{l_2^2+m_2^2+n_2^2}}$ Here $l_1=1,m_1=1,n_1=1$ and $l_2=1,m_2=-1,n_2=n$ and $\theta =60^{\circ }$ $\therefore \cos 60^{\circ }=\frac{1\times 1+1\times (-1)+1\times n}{\sqrt{h^2+1^2+1^2\times }\sqrt{1^2+1^2+y^2}}$ $\Rightarrow \frac{1}{2}=\frac{1}{\sqrt{3}\sqrt{2+n^2}}\Rightarrow 3\left(2+n^2\right)=4n^2$ $\Rightarrow n^2=6\Rightarrow n=\pm \sqrt{6}$