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

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.

Concept: Components of a Vector
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