Let → a = ^ i + ^ j - ^ k and → c = 2 ^ i - 3 ^ j + 2 ^ k . Then...

Given, $\overset{\to}{a} = i + j - k and$\overset{\to}{c} = 2i - 3j + 2k$</p><p>$\overset{\to}{b} \times \overset{\to}{c} = \overset{\to}{a}$and \left|\overset{\to}{b}\right| \in\left\{1, 2 \ldots \ldots 10\right\}</p><p>$∵ \overset{\to}{b} \times \overset{\to}{c} = \overset{\to}{a}$</p><p>$⇒ \overset{\to}{a}$is perpendicular to$\overset{\to}{b}$as well as$\overset{\to}{a}$is perpendicular to$\overset{\to}{c}$, so$\overset{\to}{a} \cdot \overset{\to}{c} = 0$as they are perpendicular.</p><p>Now checking$\overset{\to}{a} \cdot \overset{\to}{c} = 2 - 3 - 2 = - 3 \ne 0$</p><p>This$\overset{\to}{b} \times \overset{\to}{c} = \overset{\to}{a}$is not possible.</p><p>So, number of vectors$\overset{\to}{b} = 0$</p>$