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MHT CET202124 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

If a =3 i + j - k , b =2 i - j +23 k and c =7 i - j +23 k , then which of the following is valid.

Options

  1. Aa , b , c are mutually perpendicular
  2. Ba , b , c are non-coplanar
  3. Ca and b are collinear
  4. Da , b , c are coplanar

Correct answer

B. a , b , c are non-coplanar

Step-by-step solution

We have a =3 i + j - k , b =2 i - j +23 k and c =7 i - j +23 k a b =6-1-23 0 and b c =14+1+529 0 Thus a , b , c are non mutually perpendicular. Also for a and b , 3 2 -1 -1 23 . Thus a and b are not collinear. Now | array ccc 3 & 1 & -1 2 & -1 & 23 7 & -1 & 23 array |=3(-23+23)-(46-161)-(-2+7) 0 . Thus a , b , c are non coplanar.

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