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Let veca , vecb,vecc be three vectors s...

Let ` veca , vecb,vecc` be three vectors such that
` veca bot ( vecb + vecc), vecb bot ( vecc + veca) and vecc bot ( veca + vecb) , " if " |veca| =1 , |vecb| =2 `,
` |vecc| =3 , " then " | veca + vecb + vecc|` is,

A

` sqrt6`

B

14

C

` sqrt14`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
we have,
` veca bot ( vecb + vecc), vecb bot ( vecc + veca) and vecc bot ( veca + vecb) `
` Rightarrow veca.vecb + veca.vecc =0, vecb.veca =0, vecc.veca + vecc.vecb =0`
` Rightarrow veca.vecb = vecb.vecc= vecc.veca =0`
` |veca + vecb + vecc|^(2) = |veca|^(2) + 2 (veca.vecb + vecb.vecc + vecc. veca)`
` Rightarrow |veca + vecb + vecc|^(2) = 1+ 4+9 =14`
` Rightarrow |veca + vecb+ vecc| = sqrt 14`
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