If → a = ^ i + 2 ^ j + 3 ^ k , → b = - ^ i + 2 ^ j + ^ k , → c = 3...

\left(\overset{→}{a} + p\overset{→}{b}\right)$is normal to$\overset{→}{c}$</p><p>$∴ \left(\overset{→}{a} + p\overset{→}{b}\right) \cdot \overset{→}{c} = 0</p><p>\left(\left(1 - p\right)\overset{^}{i} + \left(2 + 2p\right)\overset{^}{j} + \left(3 + p\right)\overset{^}{k}\right) \cdot \left(3\overset{^}{i} + \overset{^}{j}\right) = 0

$3 - 3p + 2 + 2p = 0 ⇒ p = 5$