Two vector `vec(A) and vec(B) are vec(A)=5hati+3hatj-4hatk and vec(B)=5hati+2hatj+4hatk` . Find the unit vectors along `vec(A)+vec(B) and vec(A)-vec(B)`.

Explanation

`vec(A)=5hati+3hatj-4hatk and vec(B)=5hati+2hatj+4hatk`
`therefore vec(A)+vec(B)=(5+5)hati+(3+2)hatj+(-4+4)hatk=10hati+5hatj and |vec(A)+vec(B)|=sqrt(10^2+5^2)=5sqrt(5)`
Hence, unit vector along `vec(A)+vec(B)=(vec(A)+vec(B))/(|vec(A)+vec(B)|)=2/sqrt(5)hati+1/sqrt(5)hatj`
Similarly, `vec(A)-vec(B)=hatj-8hatk and |vec(A)-vec(B)|=sqrt(1^2+(-8)^2)=sqrt(65)`
and unit vector along `vec(A)-vec(B)=(vec(A)-vec(B))/(|vec(A)-vec(B)|)=1/sqrt(65)hatj-8/sqrt(65)hatk`.