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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Consider the following three planes aligned & P₁: x=y +z & P₂: y=z +x & P₃: z=x +y aligned If P₁, P₂, P₃ intersect in the line x = y = z then the value of + + is equal to

Options

  1. A2
  2. B5 2
  3. C- 3 2
  4. D7 2

Correct answer

C. - 3 2

Step-by-step solution

If three planes pass through the same line, their normal vector will be coplanar aligned & | array ccc -1 & & & -1 & & & -1 array |=0 & ^2 + ^2 + ^2 +2 =1 aligned ....(1) Now the cross product r of normals of P₁ , and P₂ will parallel to line Direction ratio of r = | array ccc i & j & k -1 & & & -1 & array |= ( + ),( + ), (1- ^2 ) r is parallel to given line + = + = 1- ^2 = ....(2) Using (1) and (2) we get = ( + ) ( + )= ( 2 - )= + + =2 n + 2 (n z)

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