Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Three-dimensional Geometry

Question:

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

Options:

45°

30°

60°

90°

Correct Answer:

45°

Explanation:

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}}$

$cos \theta = 45°$