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Vector Algebra question

2022 · 25 Jun · Shift 2 · Q42

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JEE Main
Mathematics
Vector Algebra
2022 · 25 Jun · Shift 2 · Q42

Vector Algebra question

2022 · 25 Jun · Shift 2 · Q42

JEE MainMathematicsVector AlgebraNumerical+4 / −1

Let

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

,

\lambda\in

R. If

\overrightarrow a

is a vector such that

\overrightarrow a \times \overrightarrow b = 13\widehat i - \widehat j - 4\widehat k

and

\overrightarrow a \,.\,\overrightarrow b + 21 = 0

, then

\left( {\overrightarrow b - \overrightarrow a } \right).\,\left( {\widehat k - \widehat j} \right) + \left( {\overrightarrow b + \overrightarrow a } \right).\,\left( {\widehat i - \widehat k} \right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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