JEE MAIN - Physics (2022 - 28th July Morning Shift - No. 18)
If the projection of $$2 \hat{i}+4 \hat{j}-2 \hat{k}$$ on $$\hat{i}+2 \hat{j}+\alpha \hat{k}$$ is zero. Then, the value of $$\alpha$$ will be ___________.
Answer
5
Explanation
$$\overrightarrow A = 2\widehat i + 4\widehat j - 2\widehat k$$
$$\overrightarrow B = \widehat i + 2\widehat j + \alpha \widehat k$$
$$\overrightarrow A \,.\,\overrightarrow B = 0$$, as $$\overrightarrow A $$ should be perpendicular to $$\overrightarrow B $$
$$ \Rightarrow 2 + 8 - 2\alpha = 0$$
$$\alpha = 5$$
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