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If veca +vecb +vecc=0, |veca|=3,|vecb|=5...

If `veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7` , then find the angle between `veca and vecb`.

Text Solution

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Given , `veca+vecb+vecc=vec0`
`veca+vecb=-vecc`
`(veca+vecb).(veca+vecb)=(-vecc).(-vecc)`
`or a^(2)+b^(2)+2(veca.vecb)=c^(2)`
` or 9+25+2(veca.vecb) =49`
`or veca.vecb=15//2`
`or ab costheta=15//2or 3.5 costheta= 15//2`
`or costheta=1//2 Rightarrowtheta=pi//3`
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