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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Paragraph: Read the following write up carefully and answer the following questions: Consider a three dimensional Cartesian system with origin at O and three rectangular coordinate axes x , y and z -axis. Suppose that the distance between two points P and Q in the space having their coordinates ( x ₁, y ₁, z ₁ ) and ( x ₂, y ₂, z ₂ ) respectively be defined by the following formula d(P, Q)= |x₂-x₁ |+ |y₂-y₁ |+ |z₂-z₁

Options

  1. Aa sphere of radius k
  2. Ba set of eight planes forming an octahedron
  3. Ca set of eight planes forming hexagonal prism
  4. Dan infinite cylinder of radius k

Correct answer

B. a set of eight planes forming an octahedron

Step-by-step solution

d(O, P)=k |x|+|y|+|z|=k which represents a set of 9 planes making intercepts of lengths k on positive as well negative sides of all three axes. See the adjacent figure.

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