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Manipal MET2014MathematicsThree Dimensional Geometry

The distance of the point (1,-5,9) , from the plane r ( i - j + k )=5 measured along the line r = i + j + k is

Options

  1. A3 5
  2. B10 3
  3. C5 3
  4. D3 10

Correct answer

B. 10 3

Step-by-step solution

Let Q be the point where the line through P(1,-5,9) and parallel to r = i + j + k meets the plane r ( i - j + k )=5 . Equation of P Q , is aligned & x-1 1 & = y+5 1 = z-9 1 = & x & = +1 and y & = -5 z & = +9 aligned lies on the plane x-y+z=5 array ll & +1- +5+ +9=5 & =-10 array Co-ordinates of Q are Q(-9,-15,-1) P Q= 10^2+10^2+10^2 =10 3

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