QJEEM19Ma2558: JEE Main 2019 Physics - Class 11 JEEM19Ma2558 Solution: Let and be two vectors. If a vector perpendicular to both the…

Question

Verified Solution • 2025–26 Session moderate

Let

\overrightarrow a = 3\widehat i + 2\widehat j + 2\widehat k

and

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

be two vectors. If a vector perpendicular to both the vectors

\overrightarrow a + \overrightarrow b

and

\overrightarrow a - \overrightarrow b

has the magnitude 12 then one such vector is :

Accepted Answer

Required vector is

\overrightarrow r

=

\lambda \left( {\left( {\overline a + \overline b } \right) \times \left( {\overline a - \overline b } \right)} \right)

\Rightarrow | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 4 & 4 & 0 \\ 2 & 0 & 4 \end{matrix} | = λ (16 \hat{i} - 16 \hat{j} - 8 \hat{k})

\Rightarrow \overrightarrow r = 8\lambda \left( {2\widehat i - 2\widehat j - \widehat k} \right) = \left| {\overrightarrow r } \right|

\Rightarrow \left| {8\lambda } \right|.3 \Rightarrow 8\lambda = \pm 4

\Rightarrow \overrightarrow r = \pm 4\left( {2\widehat i - 2\widehat j - \widehat k} \right)

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