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If veca, vecb and vecc are unit vectors ...

If `veca, vecb and vecc` are unit vectors satisfying `|veca-vecb|^(2)+|vecb-vecc|^(2)+|vecc-veca|^(2)=9 " then find the value of " |2veca+ 5vecb+ 5vecc|` .

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
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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