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AP EAMCET20226 Jul 2022Evening ShiftMathematicsVector AlgebraActual

If a = i + j + k , c = j - k , a b = c , a b =3 , then b =

Options

  1. A1 3 (5 i +2 j +2 k )
  2. B1 3 (2 i +5 j +2 k )
  3. C1 3 (2 i +2 j +3 k )
  4. D1 3 (2 i +5 j +5 k )

Correct answer

A. 1 3 (5 i +2 j +2 k )

Step-by-step solution

Let b =x i +y j +z k If a b = c , then c is perpendicular to both a and b aligned b c & =0 y-z & =0 y & =z...(i) aligned Also a b =3 array r x+y+z=3 x+2 y=3...(ii) array a b = c | array ccc i & j & k 1 & 1 & 1 x & y & z array |= j - k aligned & i (z-y)- j (z-x)+ k (y-x)= j - k & x-z=1 and x-y=1...(ii) aligned Subtracting Eq. (ii) from Eq. (i), 3 y=2 y= 2 3 Also, z= 2 3 [from Eq. (i)] array cc & x+y+z=3 & x+ 4 3 =3 x= 5 3 & b = 1 3 (5 i +2 j +2 k ) array

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