Question

The angle between the lines whose direction ratios are $1$, $1$, $2$ and $\sqrt{3}-1,$ $-\sqrt{3}-1,4$ is -

• A. ${45}^0$
• B. ${30}^0$
• C. ${60}^0$
• D. ${90}^0$

Answer 1

The correct option is C ${60}^0$

Directions $1,1,2$ & $\sqrt{3}-1,-\sqrt{3}-1,4$

$\cos \theta =\frac{(\sqrt{3}-1)\left(1\right)+(-\sqrt{3}-1)\times 1+4\times 2}{\sqrt{1+1+4}\sqrt{4^2+{(\sqrt{3}-1)}^2}+{(\sqrt{3}+1)}^2}\cos \theta =\frac{6}{\sqrt{6}\times 2\sqrt{6}}=\frac{1}{2}\theta ={60}^{\circ }$