If vectors P→=ai^+aj^+3k^ and Q→=ai^−2j^−k^ are perpendicular to each other, then the positive value of a is

P→.Q→=(ai^+aj^+3k^).(ai^−2j^−k^)=0 Or a2−2a−3=0 ∴a=2±4+122=3

P→.Q→=(ai^+aj^+3k^).(ai^−2j^−k^)=0 Or a2−2a−3=0 ∴a=2±4+122=3

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If vectors $\vec{P} = a \hat{i} + a \hat{j} + 3 \hat{k}$ and $\vec{Q} = a \hat{i} - 2 \hat{j} - \hat{k}$ are perpendicular to each other, then the positive value of $a$ is

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$\vec{P} . \vec{Q} = (a \hat{i} + a \hat{j} + 3 \hat{k}) . (a \hat{i} - 2 \hat{j} - \hat{k}) = 0$

Or $a^{2} - 2 a - 3 = 0$

$∴ a = \frac{2 \pm \sqrt{4 + 12}}{2} = 3$

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