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Question

Let a,b,c be three non-coplanar vector and p,q,r be vectors defined by the relations p=b×c[abc],q=c×a[abc],r=a×b[abc] then the value of the expression (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 C 3
Solve for (a+b).p=a.b×c[abc]+b.(b×c)[abc]=[abc][abc]=1

Similarly (b+c).q=1 and (c+a).r=1

Total value =3

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