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If hati xx[(veca-hatj)xxhati]+hatjxx[(ve...

If `hati xx[(veca-hatj)xxhati]+hatjxx[(veca-hatk)xxhatj]+veckxx[(veca-veci)xxhatk]=0` , then find vector `veca`.

Text Solution

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`hatixx[(veca-vecj)xxhati]=(hati.hati)(veca-vecj)-(hati.(veca-hatj))hati`
`= veca-hatj-(hati.veca)hati`
similarly, `hatjxx[(veca-hatk)xxvecj]=veca-veck+(vecj.veca)hatj`
`hatkxx[(veca-hati)xxhatk]=veca-hati-(hatk.veca)hatj`
`hatixx[(veca-hatj)xxhati]xx[(veca-veck)xxhatj]+hatkxx[(veca-hati)xxhatk]`
`=veca-hatj-(hati.veca)hati+veca-hatk+(hatj.veca)hatj+veca-hati-(hatk.veca)hatk=0`
`3veca-(hati+hatj+hatk)-veca=0`
`veca=1/2(hati+hatj+hatk)`
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