Find the unit vector that points in the same direction as the vector from the point P=(8,2) to the point Q=(5,9)

Find vector PQ, then divide it by its magnitude.

To find the unit vector that points in the same direction as the vector from point P to point Q, we need to follow these steps:

1. Find the vector PQ by subtracting the coordinates of point P from the coordinates of point Q. In this case, PQ = Q - P.
- PQ = (5, 9) - (8, 2) = (-3, 7)

2. Calculate the magnitude of vector PQ. The magnitude of a vector (x, y) can be found using the formula: ||v|| = √(x^2 + y^2).
- ||PQ|| = √((-3)^2 + 7^2) = √(9 + 49) = √58

3. Divide the vector PQ by its magnitude to obtain the unit vector. The unit vector is obtained by dividing each component of the vector by its magnitude.
- Unit vector = PQ / ||PQ|| = (-3/√58, 7/√58)

Therefore, the unit vector that points in the same direction as the vector from point P to point Q is (-3/√58, 7/√58).