BITSAT2023MathematicsVector AlgebraActual

If a = i + j + k , a b =1 and a b = j - k , then b is

Options

Ai - j + k
B2 j - k
C2 i
Di

Correct answer

D. i

Step-by-step solution

Given a = i + j + k , a b =1 and a b = j - k , Let b =b₁ i +b₂ j +b₃ k Now, j - k = a b = | array ccc i & j & k 1 & 1 & 1 b₂ & b₂ & b₃ array | b₃-b₂=0, b₁-b₃=1, b₂-b₁=-1 b₃=b₂, b₁=b₂+1 Also, a b =1 b₁+b₂+b₃=1 3 b₂+1=1 b₂=0 b₁=1, b₃=0 Thus, b = i

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