1.

Let hat(u) = u_(1) hat(i) + u_(2) hat(j) + u_(3) hat(k) be a unit vector in R^(3) and hat(w) = (1)/(sqrt6) (hat(i) + hat(j) + 2hat(k)). Given that there exists a vector vec(v) in R^(3), such that |hat(u) + vec(v)| =1 and hat(w). (hat(u) + vec(v)) =1 Which of the following statement(s) is/are correct ?

Answer»

There is EXACTLY one CHOICE for such `vec(V)`
There are infinitely many choices from such `vec(v)`
If `hat(u)` lies in the XY plane, then `|u_(1)| = |u_(2)|`
If `hat(u)` lies in the XZ plane then `2|u_(1)| = |u_(3)|`

Answer :A::B::C::D


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