Question
If a = i + j + k , a b =1 and a b = j - k , then b is
BITSAT
Mathematics
Vector Algebra
2023
BITSAT 2023 (Memory Based Paper 1)
BITSAT Mathematics Question (2023) — Solution
Options
- A. i - j + k
- B. 2 j - k
- C. 2 i
- D. i
Answer
D. i
Step-by-step solution
Given a = i + j + k , a b =1 and a b = j - k , Let b =b_1 i +b_2 j +b_3 k Now, j - k = a b = | array ccc i & j & k \\ 1 & 1 & 1 \\ b_2 & b_2 & b_3 array | b_3-b_2=0, b_1-b_3=1, b_2-b_1=-1 b_3=b_2, b_1=b_2+1 Also, a b =1 b_1+b_2+b_3=1 3 b_2+1=1 b_2=0 b_1=1, b_3=0 Thus, b = i
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