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Mathematics · JEE | THREE DIMENSIONAL GEOMETRY
हिन्दीThe direction cosines of the line joining the points \( A(-2, 4, -5) \) and \( B(1, 2, 3) \) are \( l, m, n \). If \( \theta \) is the angle which this directed line makes with the positive \( y \)-axis, then \( \tan^2 \theta \) equals:
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Correct answer · Option A
\( \frac{73}{4} \)
Explanation
\( AB = \sqrt{3^2 + (-2)^2 + 8^2} = \sqrt{77} \). The direction cosine \( m = \cos\theta = -\frac{2}{\sqrt{77}} \). Hence \( \cos^2\theta = \frac{4}{77} \implies \tan^2\theta = \sec^2\theta - 1 = \frac{77}{4} - 1 = \frac{73}{4} \).
