Let a vector a be coplanar with vectors b = 2 i + j + k and c = i - j + k. If a is perpendicular to d = 3 i + 2 j + 6 k, and | a | = √(10). Then a possible value of [ a b c ] + [ a b d ] + [ a c d ] is equal to:

Vector Algebra: JEE Main 2021 Mathematics question

JEE Main 2021 · 22 Jul, Evening shift · Q5731

JEE Main 202122 Jul, Evening shiftMathematicsHardVector Algebra184× since 2002

Let a vector

{\overrightarrow a }

be coplanar with vectors

\overrightarrow b = 2\widehat i + \widehat j + \widehat k

and

\overrightarrow c = \widehat i - \widehat j + \widehat k

. If

{\overrightarrow a}

is perpendicular to

\overrightarrow d = 3\widehat i + 2\widehat j + 6\widehat k

, and

\left| {\overrightarrow a } \right| = \sqrt {10}

. Then a possible value of

[\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow c } \cr } ] + [\matrix{ {\overrightarrow a } & {\overrightarrow b } & {\overrightarrow d } \cr } ] + [\matrix{ {\overrightarrow a } & {\overrightarrow c } & {\overrightarrow d } \cr } ]

is equal to :