Find unit vector perpendicular to vec A and vec B where vec A = hat{i}

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3-1.Vectors

medium

Find unit vector perpendicular to $\vec A$ and $\vec B$ where $\vec A = \hat i - 2\hat j + \hat k$ and $\vec B = \hat i + 2\hat j$

A$\frac{{2\hat i + \hat j + 4\hat k}}{{\sqrt {21} }}$

B$\frac{{ - 2\hat i + \hat j + 4\hat k}}{{\sqrt {21} }}$

C$\frac{{ - 2\hat i - \hat j + 4\hat k}}{{\sqrt {21} }}$

D$\frac{{2\hat i + \hat j + 4\hat k}}{{\sqrt 5 }}$

Solution

$\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}}$
$\overrightarrow{\mathrm{C}}=-2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+4 \hat{\mathrm{k}}$
$\hat{C}=\frac{\overrightarrow{C}}{|C|}=\frac{-2 \hat{i}+\hat{j}+4 \hat{k}}{\sqrt{21}}$

Standard 11

Physics

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Find unit vector perpendicular to $\vec A$ and $\vec B$ where $\vec A = \hat i - 2\hat j + \hat k$ and $\vec B = \hat i + 2\hat j$

Solution

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