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Write the number of vectors of unit length perpendicular to both the vectors a=2i+j+2k and b=j+k - Mathematics

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Write the number of vectors of unit length perpendicular to both the vectors `veca=2hati+hatj+2hatk and vecb=hatj+hatk`

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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.

Concept: Components of a Vector
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