For any vector `veca` the value of `(vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2` is equal to (A) `4veca^2` (B) `2veca^2` (C) `veca^2` (D) `3veca^2`

Options

A. `4a^(2)`
B. `2a^(2)`
C. `a^(2)`
D. `3a^(2)`

Answer

B

Explanation

Let `a = a_1hati + a_(2) hatj + a_3hatk`
Since, `(a xx hati) . (a xx hati) = |{:(a.a,a.hati),(hati.a,1):}| = |a|^(2) - a_(1)^(2)`
Similarly , `(axxhatj)^(2) =|a|^(2) - a_2^(2)`
and `(a xx hatk)^(2) = |a|^(2) -a_(3)^(2)`
`:. (a xx hati) + (a xx hatj)^(2) + (a xx hatk)^(2) = 3|a|^(2) - (a_(1)^(2) + a_(2)^(2) + a_(3)^(2))`
`= 3|a|^(2) - |a|^(2)`
`= 2|a|^(2) = 2a^(2)`