1. **Problem Statement:** Given points B(3,5) and C(6,-9), we need to find the vector BC, its components, and its magnitude. 2. **Vector BC:** The vector from point B to point C is found by subtracting the coordinates of B from C: $$\vec{BC} = (x_C - x_B, y_C - y_B)$$ 3. **Calculate Components:** $$x_C - x_B = 6 - 3 = 3$$ $$y_C - y_B = -9 - 5 = -14$$ So, the component form of vector BC is: $$\vec{BC} = (3, -14)$$ 4. **Magnitude of Vector BC:** The magnitude (length) of a vector $\vec{v} = (x, y)$ is given by: $$|\vec{v}| = \sqrt{x^2 + y^2}$$ Applying this to $\vec{BC}$: $$|\vec{BC}| = \sqrt{3^2 + (-14)^2} = \sqrt{9 + 196} = \sqrt{205}$$ 5. **Final Answer:** - Vector BC components: $(3, -14)$ - Magnitude of BC: $\sqrt{205} \approx 14.32$ This completes the solution for vector BC.