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Q.

Let a, b , c be three non-coplanar vectors and a=b×ca b c,b=c×aa b c,c=a×ba b c. The length of the altitude of the parallelepiped formed by a, b , c  as conterminous edges, with respect to the base having a and c as its adjacent sides is

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a

a

b

1b

c

1a×c

d

c

answer is D.

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Detailed Solution

[a b c]=b×c[a b c]  c×a[a b c]  a×b[a b c] =1[a b c]3 [b×c  c×a  a×b]=1[a b c][a b c]2=1    [a b c]=1[a b c]=|a×c| h  h=1|a×c|

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