If a = 1/(√(10))(3 i + k) and b = 1/7(2 i + 3 j - 6 k), then the value of (2 a - b)[ (a × b) × (a + 2 b) ] is:

Vector Algebra: JEE Main 2011 Mathematics question

JEE Main 2011 · Annual, Paper 1 · Q5715

JEE Main 2011Annual, Paper 1MathematicsHardVector Algebra184× since 2002

\overrightarrow a = {1 \over {\sqrt {10} }}\left( {3\widehat i + \widehat k} \right)

and

\overrightarrow b = {1 \over 7}\left( {2\widehat i + 3\widehat j - 6\widehat k} \right),

then the value of

\left( {2\overrightarrow a - \overrightarrow b } \right)\left[ {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \left( {\overrightarrow a + 2\overrightarrow b } \right)} \right]

is :

JEE Main 2011 · Annual, Paper 1 · Q5715

JEE Main 2011Annual, Paper 1MathematicsHardVector Algebra184× since 2002

\overrightarrow a = {1 \over {\sqrt {10} }}\left( {3\widehat i + \widehat k} \right)

and

\overrightarrow b = {1 \over 7}\left( {2\widehat i + 3\widehat j - 6\widehat k} \right),

then the value of

\left( {2\overrightarrow a - \overrightarrow b } \right)\left[ {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \left( {\overrightarrow a + 2\overrightarrow b } \right)} \right]

is :