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Question

The length of the perpendicular from the origin to the plane passing through three non-collinear points a,b,c is

A
[a,b,c]a×b+b×c+c×a
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B
2[a,b,c]a×b+b×c+c×a
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C
[a,b,c]
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D
[a,b,c]2a×b+b×c+c×a
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Solution

The correct option is A [a,b,c]a×b+b×c+c×a
The vector equation of the plane passing through points a,b,c is
r.(a×b+b×c+c×a)=[a,b,c]
Therefore, the length of the perpendicular from the origin to this plane is given by
[a,b,c]a×b+b×c+c×a

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