Determine the direction cosines of the unit vector perpendicular to the plane passing through the origin?

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AAI ATC Junior Executive 25 March 2021 Official Paper (Shift 2)
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  1. - 6/7, 3/7, 2/7
  2. - 2/7, 6/7, 3/7
  3. - 2/7, 3/7, 6/7
  4. - 2/7, 3/7, - 6/7

Answer (Detailed Solution Below)

Option 2 : - 2/7, 6/7, 3/7
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Detailed Solution

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Given:

Equation of plane is 

Concept:

Vector equation of a plane at a distance 'd' from the origin and unit vector to normal form origin  is 

Formula Used:

Calculation:

We have,

⇒ 

⇒ 

Multiplying with -1 on both sides,

⇒ 

⇒      ----- equation (1)

So, 

Magnitude of  = 

⇒  =  =  = 7

Now, 

⇒ 

⇒ 

∴ Direction cosines of the unit vector perpendicular to the given plane are 

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