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Mathematics · JEE | THREE DIMENSIONAL GEOMETRY
हिन्दीThe acute angle \( \theta \) between the pair of lines \( \vec{r} = (2\hat{i} - 5\hat{j} + \hat{k}) + \lambda (3\hat{i} + 2\hat{j} + 6\hat{k}) \) and \( \vec{r} = (7\hat{i} - 6\hat{k}) + \mu (\hat{i} + 2\hat{j} + 2\hat{k}) \) satisfies \( \cos\theta = \)
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Correct answer · Option D
\( \frac{19}{21} \)
Explanation
\( \cos\theta = \frac{|\vec{b}_1 \cdot \vec{b}_2|}{|\vec{b}_1||\vec{b}_2|} = \frac{|(3)(1) + (2)(2) + (6)(2)|}{\sqrt{9+4+36}\sqrt{1+4+4}} = \frac{3+4+12}{7 \times 3} = \frac{19}{21} \).
