If two vectors vec{P}=hat{i}+2 m hat{j}+m hat{k} and vec{Q}=4 hat{i}-2 hat{j}+ mk are perpendicular

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3-1.Vectors

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

A

$1$

B

$-1$

C

$-3$

D

$2$

(JEE MAIN-2023)

Solution

$\overrightarrow{ P } \cdot \overrightarrow{ Q }=0$

$(\hat{i}+2 m \hat{j}+m \hat{k}) \cdot(4 \hat{i}-2 \hat{j}+m \hat{k})=0$

$\Rightarrow 4-4 m+m^2=0$

$\Rightarrow( m -2)^2=0 \Rightarrow m=2$

Standard 11

Physics

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