किसी सदिश `veca` के लिए `|vecaxxhati|^(2)+|vecaxxhatj|^(2)+|vecaxxhatk|^(2)` का मान ज्ञात कीजियें।

Options

A. `2|a|`
B. `|a|^(2)`
C. `2|a|^(2)`
D. `2a`

Answer

C

Explanation

माना `a=a_(1)hati+a_(2)hatj "तथा " |a|^(2)=a_1^(2)+a_(2)^(2)+a_(3)^2`
`therefore axxhati=|{:(,hati,hatj,hatk),(,a_(1),a_(2),a_(3)),(,1,0,0):}|=hat`अब `axxhati=|{:(,hati,hatj,hatk),(,a_(1),a_(2),a_(3)),(,1,0,0):}|=-a_(3)hati+a_(1)hatk` `i(0)-hatj(-a_(3))+hatk(-a_(2))=a_(3)hatj-a_(2)hatk`
` axxhati=|{:(,hati,hatj,hatk),(,a_(1),a_(2),a_(3)),(,1,0,0):}|=a_(2)hati-a_(1)hatj`
`therefore |axxhati|^(2)+|axxhatj|^(2)+|axxhatk|^(2)`
`=a_3^(2)+a_2^(2)+a_3^(2)+a_(2)^(2)+a_(1)^(2)=2(a_(1)^(2)+a_(2)^(2)+a_(3)^(3))=2|a|^(2)`