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AP EAMCET202124 Aug 2021Morning ShiftMathematicsVector AlgebraActual

If a , b and c be 3 non-coplanar vectors and ( a - b ),( b -2 c ) ( c +2 a )=0 , then is equal to

Options

  1. A1
  2. B1 4
  3. C0
  4. D-1 4

Correct answer

D. -1 4

Step-by-step solution

a, b, c are there non-coplanar vectors aligned & ( a - b ) [( b -2 c ) ( c +2 a )]=0 & ( a - b ) b c +2( b a )-2( c c ) & -4( c a ) =0 & ( a - b ) b c +2( b a )-4( c a ) =0 & [ a a = 0 ] & a ( b c )+2 a ( b a )-4 a ( c a ) & - b ( b c )-2 b ( b a )+4 b ( c a )=0 & [ a b c ]+2[ a b a ]-4[ a c a ]- [ b b c ] & -2 [ b b a ]+4 [ b c a ]=0 aligned We know that in scalar triple product, if two vectors are same in box then its value is 0 . aligned & [ a b c ]+2(0)-4(0)- (0)+2 (0)+4 [ b c a ]=0 & [ a b c ]=-4 [ b c a ] & 1

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