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3-1.Vectors
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यदि दो सदिश $\overrightarrow{\mathrm{P}}=\hat{\mathrm{i}}+2 m \hat{\mathrm{j}}+m \hat{k}$ व $\overrightarrow{\mathrm{Q}}=4 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\mathrm{m} \hat{\mathrm{k}}$ एक दूसरे के लम्बवत् हो तो $\mathrm{m}$ का मान होगा :-
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
