Question

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

Answer 1

Correct Answer - 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`