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Q.

The least positive integral value of $α^{2},$ for which the angle between the vectors $α \hat{i} - 2 \hat{j} + 2 \hat{k}$ and $α \hat{i} - 2 α \hat{j} - 2 \hat{k}$ is acute, is ________

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a

36

b

25

c

6

d

5

answer is B.

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Detailed Solution

$(α \hat{i} - 2 \hat{j} + 2 \hat{k}) . (α \hat{i} + 2 \hat{j} - 2 \hat{k}) > 0$

$α^{2} - 4 α - 4 > 0$

$α < 2 - 2 \sqrt{2} o r α > 2 + 2 \sqrt{2} ≃ 4.8$

The least positive integral value of $α$ is 5.

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