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MHT CET2007MathematicsThree Dimensional Geometry

Let a =2 i - j + k , b = i +2 j - k and c = i + j -2 k be three vectors. A vector in the plane of b and c whose projection on a is of magnitude 2 3 , is

Options

  1. A2 i +3 j -3 k
  2. B2 i +3 j +3 k
  3. C2 i -5 j +5 k
  4. D2 i + j +5 k

Correct answer

A. 2 i +3 j -3 k

Step-by-step solution

Any vector in the plane of b and c is r =m b + c =(m+1) i +(2 m+1) j +(-m-2) k Projection of r on a = r a | a | = | 2 3 | array l 2(m+1)-(2 m+1)+(-m-2) 6 = 2 3 -m-1= 2 array =-3 and 1 Hence, r =-2 i -5 j + k and r =2 i +3 j -3 k

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