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Let vec a , vec b , and vec c are vecto...

Let ` vec a , vec b , and vec c` are vectors such that `| vec a|=3,| vec b|=4 and | vec c|=5, and ( vec a+ vec b)` is perpendicular to ` vec c ,( vec b+ vec c)` is perpendicular to ` vec a and ( vec c+ vec a)` is perpendicular to ` vec bdot` Then find the value of `| vec a+ vec b+ vec c|` .

Text Solution

Verified by Experts

Given , `(veca+vecb)=0Rightarrowveca.vecc+vecb.vecc=0`
`(vecb+vecc).veca=0Rightarrowveca.vecb+vecc.veca=0`
`(vecc+veca).vecb=0Rightarrowvecb.vecc+veca.vecb=0`
`2(veca.vecb+vecb.vecc+vecc.veca)=0``Now, |veca+vecb+vecc|^(2)+|vecb|^(2)+|vecc|^(2)+2(veca.vecb+vecb.vecc+vecc.veca)=50`
`|veca+vecb+vecc|=5sqrt2`
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