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BITSAT2010MathematicsVector AlgebraActual

Which one of the following is the unit vector perpendicular to both ( a =- i + j + k ) and ( b = i - j + k ) ?

Options

  1. A( i + j 2 )
  2. B( k )
  3. C( j + k 2 )
  4. D( i - j 2 )

Correct answer

A. ( i + j 2 )

Step-by-step solution

According to question ( a =- i + j + k ) and ( b = i - j + k ) Then, ( a b = | array lll i & j & k -1 & 1 & 1 1 & -1 & 1 array | ) ( gathered = i [1+1]- j [-1-1]+ k [1-1]=2( i + j ) and | a b |= 4+4 =2 2 gathered ) ( Required unit vector = 2( i + j ) 2 2 = i + j 2 )

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