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Question

If ¯a,¯b,¯c are three vectors such that |¯a|=5,¯b=12,|¯c|=13 and ¯a,¯b,¯c are perpendicular to ¯b+¯c,¯c+¯a,¯a+¯b respectively, then ¯a+¯b+¯c=

A
113
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B
213
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C
132
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D
213
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Solution

The correct option is D 132
According to the condition given that ¯a¯b+¯c , ¯b¯a+¯c,¯c¯a+¯b ; we get that ¯a.¯b=¯b.¯c=¯a.¯c=0
Thus, |¯a+¯b+¯c|=a2+b2+c2+2(¯a.¯b+¯b.¯c+¯c.¯a)=a2+b2+c2=338=132

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