Find the unit vectors perpendicular to each of the following pairs of vectors:
$\to i + \to j, \to i - \to j + \to k$

\frac{1}{\sqrt{6}} (\to i - \to j - 2 \to k)

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\frac{1}{\sqrt{3}} (\to i + \to j - \to k)

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\frac{1}{\sqrt{6}} (\to i - \to j + 2 \to k)

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\frac{1}{\sqrt{3}} (\to i + \to j + \to k)

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Solution

The correct option is A $\frac{1}{\sqrt{6}} (\to i - \to j - 2 \to k)$
Cross product of two vectors $A$ and $B$ gives vector perpendicular to both $A$ and $B$
Let $A = \to i + \to j$ and $B = \to i - \to j + \to k$
$A \times B$ $= (\to i + \to j) \times (\to i - \to j + \to k) = \to i - \to j - 2 \to k$
Unit vector of $\to i - \to j - 2 \to k$ is $\frac{\to i - \to j - 2 \to k}{\sqrt{6}}$

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