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Question

The lines r=a+λ(b×c) and r=b+μ(c×a) will intersect if

A
a×c=b×c
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B
a.c=b.c
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C
b×a=c×a
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D
None of these
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Solution

The correct option is C a.c=b.c
The lines r=a+λ(b×c) and r=b+μ(c×a) pass through points a and b, respectively and are parallel to vector b×c and c×a, respectively.
Therefore, they intersect if ab,b×c and c×a are coplanar and so
(ab).{(b×c)×(c×a)}=0(ab).([bca]c[bcc]a)=0((ab).c)[bca]=0a.cb.c=0a.c=b.c

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