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BITSAT2014MathematicsDeterminantsActual

If | array ccc p & q - y & r - z p - x & q & r - z p - x & q - y & r array |=0, then the value of p x + q y + r z is

Options

  1. A0
  2. B1
  3. C2
  4. D4 pqr

Correct answer

C. 2

Step-by-step solution

| array ccc p & q - y & r - z p - x & q & r - z p - x & q - y & r array |=0 Apply R ₁ R ₁- R ₃ and R ₂ R ₂- R ₃, we get | array ccc x & 0 & - z 0 & y & - z p - x & q - y & r array |=0 x [ yr + z ( q - y )]- z [0- y ( p - x )]=0 [Expansion along first row ] x y r+z x q+y z p=2 x y z p x + q y + r z =2

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