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JEE Advanced2011MathematicsVector AlgebraActual

Let a = i + j + k , b = i - j + k and c = i - j - k be three vectors. A vector v in the plane of a and b whose projection of c is 1 3 , is given by

Options

  1. Ai -3 j +3 k
  2. B-3 i -3 j - k
  3. C3 i - j +3 k
  4. Di +3 k -3 k

Correct answer

C. 3 i - j +3 k

Step-by-step solution

Let v = a + b v =(1+ ) i +(1- ) j +(1+ ) k Projection of v on c = 1 3 array lc & v c | c | = 1 3 & (1+ )-(1- )-(1+ ) 3 = 1 3 & 1+ -1+ -1- =1 & -1=1 =2 & v =3 i - j +3 k array

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