Question
A vector perpendicular to the plane containing the vectors i -2 j - k and 3 i -2 j - k is inclined to the vector i + j + k at an angle
BITSAT
Mathematics
Vector Algebra
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Mathematics Question (2023) — Solution
Options
- A. ^ -1 14
- B. ^ -1 14
- C. ^ -1 15
- D. None of these
Answer
A. ^ -1 14
Step-by-step solution
A vector perpendicular to the plane is aligned & ( i -2 j - k ) (3 i -2 j - k ) \\ & = | array ccc i & j & k \\ 1 & -2 & -1 \\ 3 & -2 & -1 array |=-2 j +4 k \\ & unit vector a = -2 j +4 k 4+16 = -2 j +4 k 2 5 aligned Angle between the unit vector and r = i + j + k = ^ -1 r a | r | | a | = ^ -1 1 15 = ^ -1 14
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