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Let hat(u) = u(1) hat(i) + u(2) hat(j) +...

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 ?

A

There is exactly one choice for such `vec(v)`

B

There are infinitely many choices from such `vec(v)`

C

If `hat(u)` lies in the XY plane, then `|u_(1)| = |u_(2)|`

D

If `hat(u)` lies in the XZ plane then `2|u_(1)| = |u_(3)|`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
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