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If vec a , vec ba n d vec c are three ...

If ` vec a , vec ba n d vec c` are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is a.` vec a+ vec b+ vec c` b. ` vec a/(| vec a|)+ vec b/(| vec b|)+ vec c/(| vec c|)` c. ` vec a/(| vec a|^2)+ vec b/(| vec b|^2)+ vec c/(| vec c|^2)` d. `| vec a| vec a-| vec b| vec b+| vec c| vec c`

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Statement 1: vec a , vec b ,a n d vec c are three mutually perpendicular unit vectors and vec d is a vector such that vec a , vec b , vec ca n d vec d are non-coplanar. If [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a]=1,t h e n vec d= vec a+ vec b+ vec c Statement 2: [ vec d vec b vec c]=[ vec d vec a vec b]=[ vec d vec c vec a] =>vec d is equally inclined to veca,vecb,vecc.

If non-zero vectors vec aa n d vec b are equally inclined to coplanar vector vec c ,t h e n vec c can be a. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+| vec b|) vec b b. (| vec b|)/(| vec a|+| vec b|)a+(| vec a|)/(| vec a|+| vec b|) vec b c. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+2| vec b|) vec b d. (| vec b|)/(2| vec a|+| vec b|)a+(| vec a|)/(2| vec a|+| vec b|) vec b