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Comparing Vectors

Find unit vec...

Question

Find unit vector perpendicular to the plane of the vectors,
$\to A =^i - 2^j +^k$ and $\to B = 2^i -^k .$

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Solution

The vector perpendicular to these vectors is-

$\to n = \to A \times \to B = (i - 2 j + k) \times (2 i - k)$

$\to n = 2 i + 3 j + 4 k$

$⟹ n = \sqrt{4 + 9 + 16} = \sqrt{29}$

hence, unit vector is

$^n = \frac{2 i + 3 j + 4 k}{\sqrt{29}}$

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