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AP EAMCET202017 Sep 2020Evening ShiftMathematicsVector AlgebraActual

Length of the perpendicular from the origin to the plane passing through three non-collinear points with position vectors a, ( b ) and ( c ) is

Options

  1. A| [a b c ]
  2. B(|2[ abc ]| )
  3. C( | 2[a b c] |a b+b c+c a| | )
  4. D( | [a b c] |a b+b c+c a| | )

Correct answer

D. ( | [a b c] |a b+b c+c a| | )

Step-by-step solution

Vector equation of the plane passing through points with position vector ( a , b ) and ( c ) is, ( r ( a b + b c + c a )=[ a , b , c ] ) So, length of perpendicular from origin on plane is, (d= | [ a , b , c ] | a b + b c + c a | | )

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