The directed line segment u from point P(0,0) to point Q(9,12) can be represented as u = PQ = <9, 12>.
When a scalar c is multiplied to a vector, it affects the magnitude and direction of the vector. If c < 0, it means the vector will be scaled in the opposite direction.
Let's consider cu:
- If c < 0, the vector cu will be in the opposite direction of u, meaning it will point towards the third or fourth quadrant.
- Since the original vector u = <9, 12> goes towards the first quadrant (positive x and y), the opposite direction of this vector, cu, will point towards the third quadrant where x is negative and y is negative.
Therefore, the terminal point of cu lies in Quadrant III.
