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JEE Advanced2006MathematicsVector AlgebraActual

Let a = i +2 j + k , b = i - j + k , c = i + j - k . A vector coplanar to a and b has a projection along c of magnitude 1 3 , then the vector is

Options

  1. A4 i - j +4 k
  2. B4 i + j -4 k
  3. C2 i + j + k
  4. DNone of these

Correct answer

A. 4 i - j +4 k

Step-by-step solution

Let vector r be coplanar to a and b . array ll & r = a +t b & r =( i +2 j + k )+t( i - j + k )= i (1+t)+ j (2-t)+ k (1+t) array The projection of r on c = 1 3 r c | c | = 1 3 |1 (1+t)+1 (2-t)-1 (1+t)| 3 = 1 3 |2-t|= 1 t=1 or 3 When, t=1 we have r =2 i + j +2 k When, t=3 we have r =4 i - j +4 k

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