Question

An angle between the lines whose direction cosines are given by the equations, $l+3 m+5 n=0$ and $5 l m-2 m n+6 n l=0$, is (a) $\cos ^{-1}\left(\frac{1}{8}\right)$ (b) $\cos (-)$ (c) $\cos ^{-1}\left(\frac{1}{3}\right)$ (d) $\cos ^{-1}\left(\frac{1}{4}\right)$

Name: Problem 5, Chapter 26: 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Physics
Uploaded: 2021-11-05T11:02:59-08:00
Duration: 4 min 38 s
Channel: Sriparna Bhattacharjee
Description: An angle between the lines whose direction cosines are given by the equations, l+3 m+5 n=0 and 5 l m-2 m n+6 n l=0, is (a) cos^-1((1)/(8)) (b) cos(-) (c) cos^-1((1)/(3)) (d) cos^-1((1)/(4))

   An angle between the lines whose direction cosines are given by the equations, $l+3 m+5 n=0$ and $5 l m-2 m n+6 n l=0$, is 
(a) $\cos ^{-1}\left(\frac{1}{8}\right)$
(b) $\cos (-)$
(c) $\cos ^{-1}\left(\frac{1}{3}\right)$
(d) $\cos ^{-1}\left(\frac{1}{4}\right)$

43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Physics

Disha Experts 16th Edition

Chapter 26, Problem 5

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Solved by Expert Sriparna Bhattacharjee

11/05/2021

Step 1

Step 1: Given the equations of direction cosines as $l+3 m+5 n=0$ and $5 l m-2 m n+6 n l=0$. Show more…

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An angle between the lines whose direction cosines are given by the equations, $l+3 m+5 n=0$ and $5 l m-2 m n+6 n l=0$, is (a) $\cos ^{-1}\left(\frac{1}{8}\right)$ (b) $\cos (-)$ (c) $\cos ^{-1}\left(\frac{1}{3}\right)$ (d) $\cos ^{-1}\left(\frac{1}{4}\right)$

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Key Concepts

Direction Cosines

Direction cosines are the cosines of the angles that a line makes with the three coordinate axes. They uniquely determine the orientation of a line in three-dimensional space and are bound by the relation l² + m² + n² = 1, ensuring the vector is of unit length.

Line Representation in Three-Dimensional Space

Lines in space can be described by their directional properties, often using direction cosines or direction ratios. Equations involving these cosines impose constraints that define specific orientations or families of lines, facilitating the study of their geometric relationships.

Dot Product and Angle Between Lines

The angle between two lines is computed using the dot product of their normalized direction vectors. The dot product formula provides a direct means of determining the cosine of the angle between them, which is a fundamental method in vector geometry for analyzing angular relationships.

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