Find a vector of magnitude 8 units in the direction of the vector `(5hati - hatj + 2hatk)`.

Explanation

Let `" "veca=5hati-hatj+2hatk`
`therefore" "|veca|=sqrt(5^(2)+(-1)^(2)+2^(2))=sqrt(25+1+4)=sqrt(30)`
`therefore" "hata=(veca)/(|veca|)=(5hati-hatj+2hatk)/(sqrt(30))`
Hence, the vector in the direction of vector `5hati-hatj+2hatk` which has magnitude 8 units is given by
`" "8hata=8((5hati-hatj+2hatk)/(sqrt(30)))=(40)/(sqrt(30))hati-(8)/(sqrt30)hatj+(16)/(sqrt(30))hatk`