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If a+2b+3c=4, then find the least value ...

If `a+2b+3c=4,` then find the least value of `a^2+b^2+c^2dot`

Text Solution

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consider vectors `vecP=ahati+bhatj+chatkandvecq=hati+2hatj+3hatk`
`costheta= (a+2b+3c)/(sqrt(a^(2)b^(2)=c^(2))sqrt(1^(2)+2^(2)+3^(2)))`
`cos^(2)theta= ((a+2b+3c)^(2))/(14(a^(2)+b^(2)+c^(2)))le1`
`Rightarrow a^(2)+b^(2)+c^(2)ge8/7`
Hence, least value of `a^(2) + b^(2) + c^(2) is 8/7`
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