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MHT CET2017MathematicsThree Dimensional Geometry

The equation of the plane through ( − 1 , 1 , 2 ) , whose normal makes equal acute angle with co-ordinate axes is

Options

  1. Ar → ⋅ ( i ^ + j ^ + k ^ ) = 2
  2. Br → ⋅ ( i ^ + j ^ + k ^ ) = 6
  3. Cr → ⋅ ( 3 i ^ − 3 j ^ + 3 k ^ ) = 2
  4. Dr → . ( i ^ + j ^ + k ^ ) = 3

Correct answer

A. r → ⋅ ( i ^ + j ^ + k ^ ) = 2

Step-by-step solution

Equation plane passing through A ( a → ) and ⊥ to n → is r → . n → = a → . n → Here a → = - i ^ + j ^ + 2 k ^ , n → = i ^ + j ^ + k ^ ∴ r → ⋅ i ^ + j ^ + k ^ = - i ^ + j ^ + 2 k ^ . i ^ + j ^ + k ^ = 2

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