What is the unit vector perpendicular to the | vedclass

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(c) $\vec A = 2\hat i + 2\hat j - \hat k$ and $\vec B = 6\hat i - 3\hat j + 2\hat k$

$\vec C = \vec A 	imes \vec B = \left( {2\hat i +2\hat j - \h

Vedclass · Accepted Answer

$\frac{{\hat i - 10\hat j - 18\hat k}}{{5\sqrt {17} }}$

Vedclass · Answer

(c) $\vec A = 2\hat i + 2\hat j - \hat k$ and $\vec B = 6\hat i - 3\hat j + 2\hat k$

$\vec C = \vec A 	imes \vec B = \left( {2\hat i +2\hat j - \hat k} ight) 	imes \left( {6\hat i - 3\hat j + 2\hat k}ight)$

$ = \left| {\,\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\2&2&{ - 1}\6&{ - 3}&2\end{array}\,} ight|$$ = \hat i - 10\hat j - 18\hat k$

Unit vector perpendicular to both $\vec A$ and $\vec B$

$ = \frac{{\hat i - 10\hat j - 18\hat k}}{{\sqrt {{1^2} + {{10}^2} + {{18}^2}} \,}}$

$ = \frac{{\hat i - 10\hat j - 18\hat k}}{{5\sqrt {17} }}$

What is the unit vector perpendicular to the following vectors $2\hat i + 2\hat j - \hat k$ and $6\hat i - 3\hat j + 2\hat k$

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