Comprehension

Direction: Consider the following for the items that follow:

Let S be the line of intersection of two planes x + y + z = 1 and 2x + 3y - 4z = 8.  

Which of the following are the direction ratios of S? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 〈-7, -6, 1〉
  2. 〈-7, 6, 1〉
  3. 〈-6, 5, 1〉
  4. 〈6, 5, 1〉

Answer (Detailed Solution Below)

Option 2 : 〈-7, 6, 1〉
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Detailed Solution

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Explanation:

Given:

⇒ Two planes are x + y + z = 1 and 2x + 3y – 4z = 8.

Let a, b, c are direction ratios of lines of intersection of planes.

Then the lines is perpendicular to normal of both planes

⇒ a + b + c = 0 ...(i)

⇒ 2a + 3b – 4c = 0 ....(ii) 

⇒ \(\frac{a}{-4-3} = \frac{b}{2+4} = \frac{c}{3-2} = λ \)

⇒  a = – 7λ, b = 6λ  c = λ 

Thus, Direction ratios are (–7, 6, 1).  

∴ Option (b) is correct

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