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KCET2022MathematicsThree Dimensional Geometry

The distance of the point whose position vector is (2 i + j - k ) from the plane r ( i -2 j +4 k )=4 is

Options

  1. A8 21
  2. B8 21
  3. C- 8 21
  4. D- 8 21

Correct answer

A. 8 21

Step-by-step solution

Equation of plane r ( i -2 j +4 k )=4 aligned & r n =d & Point a =2 i + j - k & n = i -2 j +4 k , d=4 & Distance = | a n -d| | n | = | (2 i + j - k ) ( i -2 j +4 k )-4 1^2+(-2)^2+4^2 | & = | 2-2-4-4 1+4+16 |= | -8 21 |= 8 21 & aligned

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