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Question

If the vectors (bc,b2+bc,c2+bc),(a2+ac,ac,c2+ac) and (a2+ab,b2+ab,ab) are coplanar, where none of a, b or c is zero, then

A
a2+b2+c2=1
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B
bc+ca+ab=0
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C
a+b+c=0
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D
a2+b2+c2=bc+ca+ab
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Solution

The correct option is B bc+ca+ab=0
(bc,b2+bc,c2+bc),(a2+ac,ac,c2+ac) and (a2+ab,b2+ab,ab)
are co-planar when
∣ ∣ ∣bcb2+bcc2+bca2+acacb2+aca2+abb2+abab∣ ∣ ∣=0∣ ∣ ∣bcb2c2a2acc2a2b2ab∣ ∣ ∣+∣ ∣0bcbcac0acabab0∣ ∣=0bc+ac+ab=0

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