If `| vec a|=2,` then find the value of `| vec axx hat i|^2+| vec axx hat j|^2+| vec axx hat k|^2dot`

Explanation

`|vecaxxveci|^(2)=|{:(hati,hatj,hatk),(a_(1),a_(2),a_(3)),(1,0,0):}|^(2)`
`=|a_(3)hatj-a_(2)hatk|^(2)=a_(3)^(2)+a_(2)^(2)`
similarly, `|vecaxxvecj|^(2)=a_(1)^(2)+a_(3)^(2) and|vecaxxveck|^(2)=a_(1)^(2)+a_(2)^(2)`
Hence, the required result can be given as `2(a_(1)^(2)+a_(2)^(2)+a_(3)^(2))=2|veca|^(2)=8`