If `vec(e_1) , vec(e_2) , vec(e_3)` and `vec(e_1) , vec(e_2), vec(e_3)` , are two sets of non-coplanar vectors

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Q 2272867736.     If `vec(e_1) , vec(e_2) , vec(e_3)` and `vec(e_1) , vec(e_2), vec(e_3)` ,


are two sets of non-coplanar vectors
such that for `i = 1, 2, 3` we have

`vec(e_i), * vec(e_j') = { tt ( (1, text (if) i= j) , (0, text (if) i ne j) )`

then the value of

`[ 3 vec(e_1) 5 vec(e_2) 7 vec(e_3) ]`

`[ 2 vec(e'_1) 4 vec(e'_2 ) 6 vec(e'_3) ] ` must be

HINT


Solution
(Provided By a Student and Checked/Corrected by EXXAMM.com Team)

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