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AP EAMCET201923 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

If ( a = i + j + k , b = i + j +2 k ) and ( c =2 i +3 j +4 k ) then the magnitude of the projection on ( c ) of a unit vector that is perpendicular to both ( a ) and ( b ) is

Options

  1. A( 1 29 3 )
  2. B( 1 6 )
  3. C( 1 58 )
  4. D( 3 29 )

Correct answer

C. ( 1 58 )

Step-by-step solution

Given vectors are ( a = i + j + k , b = i + j +2 k and c =2 i +3 j +4 k ) Then, ( a b = | array ccc i & j & k 1 & 1 & 1 1 & 1 & 2 array | ) (= i (2-1)- j (2-1)+ k ( l -1)= i - j ) So, unit vector perpendicular to both ( a ) and ( b ) is (= i - j 2 ) Now the magnitude of the projection of ( i - j 2 ) on ( c ) is ( aligned & = | ( i - j 2 ) (2 i +3 j +4 k ) 4+9+16 | & = | 2-3 2 29 |= 1 58 aligned ) Hence, option (c) is correct.

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