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Vector Algebra question

2016 · Shift 2 · Q21

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PYQ Library
JEE Advanced
Mathematics
Vector Algebra
2016 · Shift 2 · Q21

Vector Algebra question

2016 · Shift 2 · Q21

JEE AdvancedMathematicsVector AlgebraMultiple correct+4 / −2

Let

\widehat u = {u_1} \widehat i + {u_2}\widehat j + {u_3}\widehat k

be a unit vector in

{{R^3}}

and

\widehat w = {1 \over {\sqrt 6 }}\left( {\widehat i + \widehat j + 2\widehat k} \right).

Given that there exists a vector

{\overrightarrow v }

in

{{R^3}}

such that

\left| {\widehat u \times \overrightarrow v } \right| = 1

and

\widehat w.\left( {\widehat u \times \overrightarrow v } \right) = 1.

Which of the following statement(s) is (are) correct?

A
There is exactly one choice for such ${\overrightarrow v }$
B
There are infinitely many choices for such ${\overrightarrow v }$
C
If $\widehat u$ lies in the $xy$ -plane then $\left| {{u_1}} \right| = \left| {{u_2}} \right|$
D
If $\widehat u$ lies in the $xz$ -plane then $2\left| {{u_1}} \right| = \left| {{u_3}} \right|$

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