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If vec a , vec b , vec c are mutually p...

If ` vec a , vec b , vec c` are mutually perpenedicular vectors of equal magnitudes, show that the vector ` vec a+ vec b+ vec c` is equally inclined to ` vec a , vec b ,a n d vec cdot`

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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.