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Question

Let u,v and w be vectors such that u+v+w=0. If |u|=3,|v|=4 and |w|=5, then u.v+v.w+w.u is equal to

A
0
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B
25
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C
25
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D
50
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E
47
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Solution

The correct option is B 25
Given, |u|=3,|v|=4 and |w|=5

Also, u+v+w=0

On squaring both sides, we get

|u|2+|v|2+|w|2+2(u.v+v.w+w.u)=0

32+42+52+2(u.v+v.w+w.u)=0

9+16+25+2(u.v+v.w+w.u)=0

u.v+v.w+w.u=502=25

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