QJEEM22Phb0fb: JEE Main 2022 Physics - Class 11 JEEM22Phb0fb Solution: If the projection of 2 i ^ + 4 j ^ − 2 k ^ on i ^ + 2 j ^ + α k …

Question

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If the projection of $2 \hat{i} + 4 \hat{j} - 2 \hat{k}$ on $\hat{i} + 2 \hat{j} + α \hat{k}$ is zero. Then, the value of $α$ will be ___________.

Accepted Answer

$\vec{A} = 2 \hat{i} + 4 \hat{j} - 2 \hat{k}$

$\vec{B} = \hat{i} + 2 \hat{j} + α \hat{k}$

$\vec{A} . \vec{B} = 0$ , as $\vec{A}$ should be perpendicular to $\vec{B}$

$\Rightarrow 2 + 8 - 2 α = 0$

$α = 5$

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