The value of (a×b)⋅(c×d)+(b×c)⋅(a×d)+(c×a)⋅(b×d) is
A
0
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B
3
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C
2
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D
-3
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Solution
The correct option is A 0 (a×b)⋅(c×d)=(a.c)(b.d)−(a.d)(b.c) (b×c)⋅(a×d)=(b.a)(c.d)−(b.d)(c.a) (c×a)⋅(b×d)=(c.b)(a.d)−(c.d)(a.b) ∴(a×b)⋅(c×d)+(b×c)⋅(a×d)+(c×a)⋅(b×d)=0