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AP EAMCET201920 Apr 2019Evening ShiftMathematicsVector AlgebraActual

Let a =2 i -3 j +4 k , b = i +2 j -2 k and c =3 i - j + k . The volume (in cubic units) of the parallelopiped having a + b + c , a - b + c and a + b - c as coterminus edges is

Options

  1. A6
  2. B7
  3. C28
  4. D36

Correct answer

C. 28

Step-by-step solution

It is given that, a =2 i -3 j +4 k , b = i +2 j -2 k and c =3 i - j + k So, vectors aligned a + b + c & =6 i -2 j +3 k a - b + c & =4 i -6 j +7 k and a + b - c & =0 i -0 j + k aligned So, the required volume of the parallelopiped having a + b + c , a - b + c and a + b - c as coterminus edges is v= | array ccc 6 & -2 & 3 4 & -6 & 7 0 & 0 & 1 array |=|1(-36+8)|=|-28|=28 . Hence, option (c) is correct.

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