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Question

If a and b are not perpendicular to each other and r×a=b×a,r.c=0 then r is equal to

A
ac
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B
b+xa for all scalar c
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C
bb.ca.c.a
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D
None of these
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Solution

The correct option is B bb.ca.c.a
Since r×a=b×a(rb)×a=0
rb is parallel to a
rb=λa for some scalar λ
r=b+λa ...(1)
Now, rcr.c=0(b+λa).c=0
b.c+λ(a.c)=0λ=b.ca.c
Putting the value of λ in (1), we get
r=bb.ca.ca

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