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If a = 2i + j - 3k and b = i - 2j + k, find a vector of magnitude 5 perpendicular to both a and b.

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Given :

a = 2i + j - 3k

\(\overline{a} = 2\hat{i} + \hat{j} - 3\hat{k}\) and \(\overline{b} = \hat{i} - 2\hat{j} + \hat{k}\)

∴ unit vectors perpendicular to both the vectors \(\overline{a}\) and \(\overline{b}.\)

∴ required vectors of magnitude 5 units

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