Let a = i + 5 j + α k, b = i + 3 j + β k and c = - i + 2 j - 3 k be three vectors such that, | b × c | = 5 3 and a is perpendicular to b. Then the greatest amongst the values of | a |² is _ _ _ _ _ _ _.

Vector Algebra: JEE Main 2021 Mathematics question

JEE Main 2021 · 27 Aug, Morning shift · Q51

JEE Main 202127 Aug, Morning shiftMathematicsHardVector Algebra184× since 2002

Let

\overrightarrow a = \widehat i + 5\widehat j + \alpha \widehat k

\overrightarrow b = \widehat i + 3\widehat j + \beta \widehat k

and

\overrightarrow c = - \widehat i + 2\widehat j - 3\widehat k

be three vectors such that,

\left| {\overrightarrow b \times \overrightarrow c } \right| = 5\sqrt 3

and

{\overrightarrow a }

is perpendicular to

{\overrightarrow b }

. Then the greatest amongst the values of

{\left| {\overrightarrow a } \right|^2}

is _____________.

Your answerType your answer. Integers and decimals are accepted.