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If a, b, c are mutually perpendicular unit vectors, the value of a · (b × c) is
A±1
B0
C3
D1/3
Answer & Solution
Correct answer: A. ±1
1. b × c gives a vector perpendicular to both b and c with magnitude |b||c| sin 90° = 1.
2. Since a is mutually perpendicular too, a is parallel (or anti-parallel) to b × c.
3. Hence a · (b × c) = ±|a| × 1 = ±1.
_Source: Maharashtra Balbharati Std XII Mathematics Part 1, Ch 5 "Vectors" §5.6_
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