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AP EAMCET2012MathematicsThree Dimensional Geometry

Let a = i +2 j + k , b = i - j + k , c = i + j - k . A vector in the plane of a and b has projection 1 3 on c. Then, one such vector is

Options

  1. A4 i + j -4 k
  2. B3 i + j -3 k
  3. C4 i - j +4 k
  4. D2 i + j +2 k

Correct answer

D. 2 i + j +2 k

Step-by-step solution

Since, vectors a and b are in a same plane. aligned r & = a +t b & =( i +2 j + k )+t( i - j + k ) & =(1+t) i +(2-t) j +(1+t) k aligned Projection of r on c = r c | c | 1 3 = [ array c (1+t) i +(2-t) j +(1+t) k ( i + j - k ) array ] 1^2+1^2+(-1)^2 1 3 = 1+t+2-t-(1+t) 3 1=2-t t=1 On putting t=1 in Eq. (i), we get r =2 i + j +2 k

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