यदि `vec(a)=i-2hatj+3hatk` तथा `vec(b)=2hati+3hatj-5hatk` तो `vec(a)xx vec(b)` ज्ञात करें तथा सत्यापित करें कि `vec(a)xx vec(b), vec(a)` तथा `vec(b)` में से प्रत्येक पर लम्ब है |

Explanation

दिया है, `vec(a)=hati-2hatj+3hatk,vec(b)=2hati+3hatj-5hatk`
`:." "vec(a)xx vec(b)=|{:(hati,,hatj,,hatk),(1,,-2,,3),(2,,3,,-5):}|`
`=(10-9)hati-(-5-6)hatj+(3+4)hatk=hati+11hatj+7hatk`.
अब, `(vec(a)xx vec(b))cdot vec(a)=(hati+11hatj+7hatk)cdot (hati-2hatj+3hatk)`
`=1-22+21=0`.
`:." "(vec(a)xx vec(b))_|_ vec(a)`
पुन:, `(vec(a)xx vec(b))cdot vec(b)=(hati+11hatj+7hatk)cdot(2hati+3hatj-5hatk)=2+33-35=0`
`:." "(vec(a)xx vec(b))_|_ vec(b)`.