Let ` vecu = u_(1)hati + u_(2)hatj +u_(3)hatk` be a unit vector in ` R^(3) and vecw = 1/sqrt6 ( hati + hatj + 2hatk)` , Given that there exists a vector `vecv " in " R^(3)` such that ` | vecu xx vecv| =1 and vecw . ( vecu xx vecv) =1` which of the following statements is correct ? (a)there is exactly one choice for such `vecv` (b)there are infinitely many choices for such `vecv` (c)if `hatu` lies in the xy - plane then `|u_(1)|=|u_(2)|` (d)if `hatu` lies in the xz-plane then `2|u_(1)|=|u_(3)|`

Options

A. there is exactly one choice for such `vecv`
B. There are infinintely many choices for such `vecv`
C. if `vecu` lies in the xy-plane then `|u_(1)|=|u_(2)|`
D. If `vecu` lies in the xy-plane then `2|u_(1)|=|u_(3)|`

Answer

B, C