Comprehension

The projections of a directed line segment on the coordinate axes are 12, 4, 3 respectively.

What are the direction cosines of the line segment?

This question was previously asked in
NDA (Held On: 19 Apr 2015) Maths Previous Year paper
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  1. {12/13, 4/13, 3/13}
  2. {12/13, -4/13, 3/13}
  3. {12/13, -4/13, -3/13}
  4. {-12/13, -4/13, 3/13}

Answer (Detailed Solution Below)

Option 1 : {12/13, 4/13, 3/13}
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NDA 01/2025: English Subject Test
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Detailed Solution

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Concept:

  • Relation between direction cosines and direction ratios

 

Where l, m, n are the direction cosines and a, b, c are the direction ratios.

Calculation:

We know that direction cosines is

Here a = 12, b = 4 and c = 3

Now,

∴ Direction cosines of the line segment = {12/13, 4/13, 3/13}

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