Let a = 2 i + j - 2 k and b = i + j. If c is a vector such that a. c = | c |,| c - a | = 2 2 and the angle between (a × b) and c is (π)/6, then the value of | (a × b) × c | is:

Vector Algebra: JEE Main 2021 Mathematics question

JEE Main 2021 · 20 Jul, Morning shift · Q5730

JEE Main 202120 Jul, Morning shiftMathematicsMediumVector Algebra184× since 2002

Let

\overrightarrow a = 2\widehat i + \widehat j - 2\widehat k

and

\overrightarrow b = \widehat i + \widehat j

. If

\overrightarrow c

is a vector such that

\overrightarrow a .\,\overrightarrow c = \left| {\overrightarrow c } \right|,\left| {\overrightarrow c - \overrightarrow a } \right| = 2\sqrt 2

and the angle between

(\overrightarrow a \times \overrightarrow b )

and

\overrightarrow c

{\pi \over 6}

, then the value of

\left| {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c } \right|

is :