What is the cosine of angle between the planes x + y + z + 1 = 0 and 2x - 2y + 2z + 1 = 0?

  1. 1/2
  2. 1/3
  3. 2/3
  4. None of the above

Answer (Detailed Solution Below)

Option 2 : 1/3
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NDA 01/2025: English Subject Test
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Detailed Solution

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Concept:

 The angle between the two planes a1x + b1y + c1z + d= 0 and a2x + b2y + c2z + d2 = 0 is given by 

Calculations:

Given planes are,  x + y + z + 1 = 0 ⇒ a1x + b1y + c1z + d= 0

and 2x - 2y + 2z + 1 = 0 ⇒ a2x + b2y + c2z + d2 = 0 

We know that the angle between the two planes a1x + b1y + c1z + d= 0 and a2x + b2y + c2z + d2 = 0 is given by 

⇒ 

⇒ 

 

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