Question

How do you find a unit vector from the point P=(1,1) and toward the point Q=(4,5)?

Answer 1

The unit vector is `=〈3/5,4/5〉`

Explanation:

The vector `vec(PQ)=〈(4-1),(5-1)〉=〈3,4〉`
The modulus of vector `∥vec(PQ)∥=sqrt(a^2+b^2)=sqrt(9+16)=5`

The unit vector is given by `hat(PQ)=vec(PQ)/(∥vec(PQ)∥)=1/5〈3,4〉`