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If vec e1, vec e2, vec e3a n d vec E1, ...

If ` vec e_1, vec e_2, vec e_3a n d vec E_1, vec E_2, vec E_3` are two sets of vectors such that ` vec e_idot vec E_j=1,ifi=j` and `vec e_idot vec E_j=0a n difi!=j ,` then prove that `[ (vec e_1, vec e_2 ,vec e_3)][ (vec E_1, vec E_2, vec E_3) ]=1.`

Text Solution

Verified by Experts

we know that
`[vece_(1)vece_(2)vece_(3)][vecE_(1) vecE_(2)vecE_(3)]=|{:(vece_(1).vecE_(1),vece_(1).vecE_(2),vece_(1).vecE_(3)),(vece_(2).vecE_(1),vece_(2).vecE_(2),vece_(2).vecE_(2)),(vece_(3).vecE_(1),vece_(3).vecE_(2),vece_(3).vecE_(3)):}|`
`=|{:(1,0,0),(0,1,0),(0,0,1):}|`
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