Final answer:
To determine a unit vector in the direction of pq, subtract the coordinates of point p from the coordinates of point q to get pq. Divide pq by its magnitude to find the unit vector.
Step-by-step explanation:
To find a unit vector in the direction of pq, we first need to find the vector pq. The vector pq is found by subtracting the coordinates of point p from the coordinates of point q. In this case, pq = q - p = (-9, 11) - (7, -1) = (-16, 12).
To find the unit vector in the direction of pq, we divide the vector pq by its magnitude. The magnitude of pq is found using the formula: magnitude = sqrt((x^2) + (y^2)), where x and y are the coordinates of pq. In this case, the magnitude of pq is sqrt((-16^2) + (12^2)) = sqrt(256 + 144) = sqrt(400) = 20.
Finally, we divide the vector pq by its magnitude to get the unit vector. The unit vector in the direction of pq is (-16/20, 12/20) = (-0.8, 0.6).