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KCET2026MathematicsVector Algebra

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

Options

  1. A5 3 i - 2 3 j + 2 3 k
  2. B5 3 i + 2 3 j - 2 3 k
  3. C5 3 i + 2 3 j + 2 3 k
  4. D- 5 3 i + 2 3 j + 2 3 k

Correct answer

C. 5 3 i + 2 3 j + 2 3 k

Step-by-step solution

Given a c = b Taking the cross product with a on both sides: a ( a c ) = a b Using the vector triple product expansion: ( a c ) a - ( a a ) c = a b We are given a c = 3 . Also, a a = (1)^2 + (1)^2 + (1)^2 = 3 . Substituting these values: 3 a - 3 c = a b 3 c = 3 a - ( a b ) c = a - 1 3 ( a b ) Now, calculating a b : a b = vmatrix i & j & k 1 & 1 & 1 0 & 1 & -1 vmatrix = i (-1 - 1) - j (-1 - 0) + k (1 - 0) = -2 i + j + k Substituting a and a b into the equation for c : c = ( i + j + k ) - 1 3 (-2 i + j + k ) c = (1 +

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