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Question : 5 of 120
Marks:
+1,
-0
Solution:
According to the given condition, each vector is perpendicular to the sum of two vectors.
∴‌‌a⋅(b+c)=0 b⋅(a+c)=0 and
c⋅(a+b)=0 ⇒‌‌a⋅b+a⋅c=0,b⋅a+b⋅c=0
and câ‹…a+câ‹…b=0
⇒2(a⋅b+b⋅c+c⋅a)=0 ⇒‌‌a⋅b+b⋅c+c⋅a=0....(i)
Now
|a+b+c|2=|a|2+|b|2+|c|2
Now, |a+b+c|2=|a|2+|b|2+|c|2+2(aâ‹…b+bâ‹…c+câ‹…a)
=|a|2+|b|2+|c|2+2(0)‌‌ [From Eq. (i)]
=|a|2+|b|2+|c|2
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