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BITSAT2024MathematicsVector AlgebraActual

Let a = i - k , b =x i + j +(1-x) k and c =y i +x j +(1+x-y) k . Then, [ a b ~ c ] depends on

Options

  1. Aonly y
  2. Bonly x
  3. Cboth x and y
  4. Dneither x nor y

Correct answer

D. neither x nor y

Step-by-step solution

Here, [a b c]=|a (b c)| Now, according to question, aligned [ array lll a & b c array ] & = | array ccc 1 & 0 & -1 x & 1 & 1 - x y & x & 1+x-y array | & =1(1+x-y-x(1-x))-1 (x^2-y ) & =1+x-y-x+x^2-x^2+y & =1 & = Independent of x and y . aligned

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