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JEE Main202125 Jul 2021Evening ShiftMathematicsVector AlgebraActual

Let a , b and c be distinct positive numbers. If the vectors a i ^ + a j ^ + c k ^ , i ^ + k ^ and c i ^ + c j ^ + b k ^ are co-planar, then c is equal to:

Options

  1. A2 1 a + 1 b
  2. Ba + b 2
  3. C1 a + 1 b
  4. Da b

Correct answer

D. a b

Step-by-step solution

Given vectors a i ^ + a j ^ + c k ^ , i ^ + k ^ and c i ^ + c j ^ + b k ^ are co-planar, then a a c 1 0 1 c c b = 0 ⇒ a 0 - c - a b - c + c c - 0 = 0 ⇒ c 2 = a b ⇒ c = a b .

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