The angle between the lines whose direction ratios are proportional to 1, 1, 2 and $\sqrt{3}-1, - \sqrt{3}-1, 4,$ is
Answer & explanation
Correct answer: option 1
Let $\theta $ be the angle between the given lines. Then,
$ cos \theta = \frac{1× (\sqrt{3}-1)+1×(-\sqrt{3}-1)+2×4}{\sqrt{1+1+4}\sqrt{(\sqrt{3}-1)^2+(-\sqrt{3}-1)^2+4}}=\frac{1}{\sqrt{2}}$
$cos \theta = 45°$