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Question
Write the number of vectors of unit length perpendicular to both the vectors `veca=2hati+hatj+2hatk and vecb=hatj+hatk`
Solution
Unit vectors perpendicular to `veca and vecb are +-((vecaxxvecb)/|vecaxxvecb|)`
`vecaxxvecb=|[hati,hatj,hatk],[2,1,2],[0,1,1]|=-hati-2hatj+2hatk`
∴ Unit vectors perpendicular to `veca and vecb` are `+-(-hati-2hatj+2hatk)/sqrt((-1)^2+(-2)^2+(2)^2)=+-(-1/3hati-2/3hatj+2/3hatk)`
Thus, there are two unit vectors perpendicular to the given vectors.
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