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Vector Algebra question

2021 · 27 Aug · Shift 1 · Q34

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PYQ Library
JEE Main
Mathematics
Vector Algebra
2021 · 27 Aug · Shift 1 · Q34

Vector Algebra question

2021 · 27 Aug · Shift 1 · Q34

JEE MainMathematicsVector AlgebraNumerical+4 / −1

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

\underline{\hspace{2cm}}

.

Numerical answer

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