Define the points \( Q(3,0) \) and \( R(-5,6) \). Carry out the following calculation. Find the unit vector with the same direction as \( \overrightarrow{Q R} \).

To find the unit vector in the direction of the vector \(\overrightarrow{QR}\), follow these steps: 1. **Determine the Vector \(\overrightarrow{QR}\):** Given points: \[ Q(3, 0) \quad \text{and} \quad R(-5, 6) \] The vector \(\overrightarrow{QR}\) is calculated by subtracting the coordinates of \(Q\) from \(R\): \[ \overrightarrow{QR} = R - Q = (-5 - 3, 6 - 0) = (-8, 6) \] 2. **Calculate the Magnitude of \(\overrightarrow{QR}\):** The magnitude \(|\overrightarrow{QR}|\) is given by: \[ |\overrightarrow{QR}| = \sqrt{(-8)^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \] 3. **Find the Unit Vector:** A unit vector in the direction of \(\overrightarrow{QR}\) is obtained by dividing each component of \(\overrightarrow{QR}\) by its magnitude: \[ \mathbf{u} = \left( \frac{-8}{10}, \frac{6}{10} \right) = \left( -\frac{4}{5}, \frac{3}{5} \right) \] So, the unit vector in the direction of \(\overrightarrow{QR}\) is: \[ \mathbf{u} = \left( -\frac{4}{5}, \frac{3}{5} \right) \] **Final Answer:** After simplifying, a unit vector in the direction of QR is ( –4⁄5,  3⁄5 ).