Let u^{∧}=u_1i^{∧}+u_2j^{∧}+u_3k^{∧} be a unit vector in R^2 and w^{∧}=1/\sqrt6(i^{∧}+j^{∧}+2k^{∧}).Given n that there exists a vector v^{\to} in R^3 such that |u^{∧}\timesv^{\to}|=1 and w^{∧}·(u^{∧}\timesv^{\to})=1.which of the following statement(s) is(are) correct? [JEE Adv 2016 P2]

There is exactly one choice for such v^{\to}

There are infinitely many choice for such v^{\to}

If u^{∧} lies in the xy-plane then |u_1|=|u_2|

If u^{∧} lies in the xy-plane then 2|u_1|=|u_3|

Vector Algebra

Section: Mathematics

Question : 17 of 38

Marks: +1, -0

Let

∧

=u1

∧

+u2

∧

+u3

∧

be a unit vector in R2 and

∧

√6

(

∧

).Given n that there exists a vector

→

in R3 such that |

∧

→

|=1 and

∧

·(

∧

→

)=1.which of the following statement(s) is(are) correct?

[JEE Adv 2016 P2]

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