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Question

a,b,c are noncoplanar vectors and p,p,r as defined as
p=b×c[bca],q=c×a[cab],r=a×b[abc],(a+b).p+(b+c).q+(c+a).r is equal to

A
0
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B
1
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C
2
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D
3
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Solution

The correct option is B 3
(a+b)(b+c)[bca]+(b+c)(c×a)[cab]+(c+a)(a×b)[abc]
=a(b×c)[bca]+0+b(c×d)[cab]+0+c(a×b)[abc]+0
=[abc][bca]+[bca][cab]+[cab][abc]
=1+1+1=3

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