Find unit vector in the direction of vector `hati+hatj+2hatk`

Explanation

Given, `a=hat(i)+hat(j)+2hat(k)` comparing with `x=ahat(i)+bhat(j)+chat(k)`, we get `a=1,b=1,c=2`
Magnitude of vector `vec( a) =|vec(a)|=sqrt(a^2+b^2+c^2)= sqrt(1^2+1^2+2^2)=sqrt(6)`.
`therefore` The unit vector `hat(a)` in the direction of vector `a=hat(i)+hat(j)+2hat(k)` is given by
`hat(a)=(a)/(|a|)=(1)/(sqrt(6))(hat(i)+hat(j)+hat(k))=(1)/(sqrt(6))hat(i)+(1)/(sqrt(6))hat(j)+(2)/(sqrt(6))hat(k)`.