दो सदिशों `(2hati+3hatj+hatk` तथा `(hati-hatj+2hatk)` के लम्बवत एकांक सदिश ज्ञात कीजिए।

Options

A. `hatn=+-1/(sqrt(42))(7hati-5hatj-2hatk)`
B. `hatn=+-1/(sqrt(83))(7hati+3hatj+5hatk)`
C. `hatn=+-1/(sqrt(83))(7hati-3hatj-5hatk)`
D. `hatn=+-1/(sqrt15))(7hati-3hatj-5hatk)`

Answer

C

Explanation

माना कि `vecA=2hati+3hatj+hatk` तथा `vecB=hati-hatj+2hatk`
`hatn=+-(vecAxxvecB)/(|vecAxxvecB|)" "hatn` एक एकांक सदिश है जो `vecA` और `vecB` दोनों के लम्बवत है
`vecAxxvecB=|(hati,hatj,hatk),(2,3,1),(1,-1,2)|=hati(6+1)-hatj(4-1)+hatk(-2-3)=7hati-3hatj-5hatk`
`:.|vecAxxvecB|=sqrt(7^(2)+(-3)^(2)+(-5)^(2))=sqrt(83)` इकाई `hatn=+-1/(sqrt(83))(7hati-3hatj-5hatk)`