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If veca.veci=veca.(hati+hatj)=veca.(hati...

If `veca.veci=veca.(hati+hatj)=veca.(hati+hatj+hatk)` . Then find the unit vector `veca`.

Text Solution

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Let `veca=xhati+yhatj+zhatk`
then `veca.hati=(xhati+yhatj+zhatk).hati=x and veca. (hati+hatj)=x+y`
`and veca.(hati+hatj=hatk)=x+y+z("given that" x=x+y=x+y+z)`
now, `x=x+y Rightarrow y =0 and x+y =x+y+z Rightarrow z=0`
Hence, x =1 ( sicne `veca` is a unit vector)
`veca=veci`
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