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Q.

Let p¯=b¯×c¯[a¯b¯c¯]q¯=a¯×c¯[a¯b¯c¯],r¯=a¯×b¯[a¯b¯c¯] and a¯,b¯,c¯  being any three non-zero, non-coplanar vectors then p¯.(a¯+b¯)+q¯.(b¯+c¯)+r¯.(c¯+a¯)=

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a

3

b

2

c

1

d

0

answer is C.

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Detailed Solution

p¯.(a¯+b¯)+q¯.(b¯+c¯)+r¯.(c¯+a¯)

 

=[a¯b¯c¯][a¯b¯c¯]+0+[a¯b¯c¯][abc]+0+[a¯b¯c¯][a¯b¯c¯]+0

=1-1+1=1

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