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Mathematics · JEE | THREE DIMENSIONAL GEOMETRY
हिन्दीThe acute angle between the lines \( \frac{x-2}{2} = \frac{y-1}{5} = \frac{z+3}{-3} \) and \( \frac{x+2}{-1} = \frac{y-4}{8} = \frac{z-5}{4} \) is:
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Correct answer · Option A
\( \cos^{-1}(\frac{26}{9\sqrt{38}}) \)
Explanation
\( \cos\theta = \frac{|a_1 a_2 + b_1 b_2 + c_1 c_2|}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2}} = \frac{|2(-1) + 5(8) + (-3)(4)|}{\sqrt{4+25+9}\sqrt{1+64+16}} = \frac{|-2 + 40 - 12|}{\sqrt{38}\sqrt{81}} = \frac{26}{9\sqrt{38}} \).
