QJEEM23Ph66d8: JEE Main 2023 Physics - Class 11 JEEM23Ph66d8 Solution: If two vectors P → = i ^ + 2 m j ^ + m k ^ and Q → = 4 i ^ − 2…

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QJEEM23Ph66d8: JEE Main 2023 Physics - Class 11 JEEM23Ph66d8 Solution: If two vectors P → = i ^ + 2 m j ^ + m k ^ and Q → = 4 i ^ − 2…

If two vectors $\vec{P} = \hat{i} + 2 m \hat{j} + m \hat{k}$ and $\vec{Q} = 4 \hat{i} - 2 \hat{j} + m \hat{k}$ are perpendicular to each other. Then, the value of m will be :

Multiple Choice Options

A −1
B 3
C 1
D 2

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Accepted Answer

\vec{P} \,\&amp;\, \vec{Q}

are perpendicular

\begin{aligned} \vec{P} \cdot \vec{Q} = 0 \\ (\hat{i} + 2 m \hat{j} + m \hat{k}) \cdot (4 \hat{i} - 2 \hat{j} + m \hat{k}) = 0 \\ \Rightarrow 4 - 4 m + m^{2} = 0 \\ \Rightarrow (m - 2)^{2} = 0 \Rightarrow m = 2 \end{aligned}

QJEEM23Ph66d8: JEE Main 2023 Physics - Class 11 JEEM23Ph66d8 Solution: If two vectors P → = i ^ + 2 m j ^ + m k ^ and Q → = 4 i ^ − 2…

Multiple Choice Options

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