1.

If ` veca. Vecb and vecc` are unit vectors satisfying ` |veca -vecb|^(2) +|vecb -vecc| ^(2) |vecc -veca| =9 , " then " |2 veca + 5 vecb + 5 vecc| ` is equal to

Answer» Correct Answer - D
we know that
` |veca + vecb + vecc|^(2) = |veca|^(2) +|vecb|^(2) +|vecc|^(2) + 2 ( veca .vecb + vecb.vecc + vecc.veca)`
` and |veca -vecb|^(2) + |vecb -vecc|^(2) +|vecc -veca|^(2) `
` = 2 (|veca|^(2) +|vecb|^(2) +|vecc|^(2) ) -2 (veca.vecb + vecb.vecc + vecc.veca)`
` |veca -vecb|^(2) + |vecb - vecc|^(2) + |vecc -veca|^(2) `
` = 3 { |veca|^(2) +|vecb|^(2) |vecc|^(2) } - |veca +vecb +vecc|^(2)`
` Rightarrow 9 = 3xx 3 - |veca + vecb + vecc|^(2) `
` Rightarrow |veca + vecb + vecc|^(2) =0`
` Rightarrow veca + vecb + vecc = vec0`
` Rightarrow vecb + vecc =- veca`
` therefore | 2 veca + 5 vecb + 5vecc| = | 2 vecb +5( -veca)| = 3|veca|=3`


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