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Most Important Selected Qs for JEE AdvancedMathematicsVector Algebra

If O A B C is a tetrahedron (where O is origin and points A, B, C lies on x, y, z axes respectively). Let A^ is point on OA ( a ), B ^ is point on OB ( b ) & C ^ is point on OC ( c ) such that A^ B ^ C ^ plane is parallel to ABC and volume of tetrahedron OA ^ B ^ C ^ is half the volume of tetrahedron OABC , then -

Options

  1. Aequation of plane through three points A^ , B^ , C^ is x | a | + y | b | + z | c | = 1 2
  2. Bequation of plane through three points A^ , B^ , C^ is x | a | + y | b | + z | c | = 1 2^ 1 / 3
  3. Carea of ( ABC ) area of ( A ^ B ^ C ^ ) =2^ 1 / 3
  4. Darea of ( ABC ) area of ( A ^ B ^ C ^ ) =2^ 2 / 3

Correct answer

C. area of ( ABC ) area of ( A ^ B ^ C ^ ) =2^ 1 / 3

Step-by-step solution

[ a b c ] 6 = 1 6 [ a ~ ~b c ] 2 = 1 2^ 1 / 3 x a + y b + z c =1 x a + y b + z c = 1 2^ 1 / 3 area ( ABC ) area ( A ^ C^ C^ ) = 1 2 ( ab )^2+( bc )^2+( ca )^2 1 2 ^2 [( ab )^2+( bc )^2+( ca )^2 ] =2^ 1 / 3

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