Find the unit vectors perpendicular to given pair of vectors: $i - j - k, i + 2 j - k,$

\frac{1}{\sqrt{2}} (i + k)

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\frac{1}{\sqrt{5}} (i + 2 k)

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\frac{1}{\sqrt{10}} (i + 3 k)

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

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Solution

The correct option is A $\frac{1}{\sqrt{2}} (i + k)$
The vector perpendicular to each, $i - j - k, i + 2 j - k,$ is,
$∣ ∣ ∣ ∣ \begin{matrix} i & j & k 1 & - 1 & - 1 1 & 2 & - 1 \end{matrix} ∣ ∣ ∣ ∣ = 3 i + 3 k$
Thus required unit vector is $\frac{1}{\sqrt{2}} (i + k)$

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