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JEE Advanced2011MathematicsVector AlgebraActual

The vector(s) which is/are coplanar with vectors i + j +2 k and i +2 j + k , are perpendicular to the vector i + j + k is/are

Options

  1. Aj - k
  2. B- i + j
  3. Ci - j
  4. D- j + k

Correct answer

A. j - k

Step-by-step solution

Let a = i + j +2 k , b = i +2 j + k and c = i + j + k A vector coplanar to a and b , and perpendicular to c . Now, ( a b ) c ( a c ) b -( b c ) a (1+1+4)( i +2 j + k )-(1+2+1)( i + j +2 k ) 6 i +12 j +6 k -6 i -6 j -12 k 6 j -6 k 6 ( j - k ) For = 1 6 Option (a) is correct. For =- 1 6 Option (d) is correct.

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