Mathematics in Physics

JEE Main level, single correct, medium

44 of 121

Question 44 of 121

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

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Answer: (B) 22

For two vectors to be perpendicular, their dot product is equal to zero.
So, P⃗⋅Q⃗=0\vec{P}\cdot \vec{Q}=0
⇒(i^+2mj^+mk^)⋅(4i^−2j^+mk^)=0⇒4−4m+m2=0⇒(m−2)2=0⇒m=2\Rightarrow \left(\hat{i}+2m\hat{j}+m\hat{k}\right)\cdot \left(4\hat{i}-2\hat{j}+m\hat{k}\right)=0 \Rightarrow 4-4m+{m}^{2}=0 \Rightarrow {\left(m-2\right)}^{2}=0 \Rightarrow m=2

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