Find a vector of magnitude 5 units, and parallel to the resultant of the vectors
`" "veca=2hati+3hatj-hatk and vecb=hati-2hatj+hatk`.

Explanation

We have,
`" "veca=2hati+3hatj-hatk and vecb=hati-2hatj+hatk`
Let `vecc` be the resultant of `veca and vecb`. Then
`" "vecc=veca+vecb=(2+1)hati+(3-2)hatj+(-1+1)hatk`
`" "=3hati+hatj`
`therefore" "|vecc|=sqrt(3^(2)+1^(2))=sqrt(9+1)=sqrt(10)`
`therefore" "hatc=(vecc)/(|vecc|)=((3hati+hatj))/(sqrt(10))`
Hence, the vector of magnitude 5 units and parallel to the resultant to vectors `veca and vecb` is
`" "pm5*vecc=pm5*(1)/(sqrt(10))(3hati+hatj)`
`" "=pm(3sqrt(10)hati)/(2)pm(sqrt(10))/(2) hatj`.