Question

let (mathbf{u} = overrightarrow{pq}) be the directed line segment from (p(0,0)) to (q(9,12)), and let (c) be a scalar such that (c < 0). which statement best describes (cmathbf{u})? the terminal point of (cmathbf{u}) lies in quadrant iii. the terminal point of (cmathbf{u}) lies in quadrant i. the terminal point of (cmathbf{u}) lies in quadrant iv. the terminal point of (cmathbf{u}) lies in quadrant ii.

Explanation:

Step1: Find vector $\vec{u}$

$\vec{u} = Q - P = (9-0, 12-0) = (9, 12)$

Step2: Calculate scalar multiple $c\vec{u}$

Since $c<0$, $c\vec{u} = (9c, 12c)$

Step3: Analyze sign of components

As $c<0$, $9c<0$ and $12c<0$. Points with both negative coordinates lie in Quadrant III.

Answer:

The terminal point of $c\vec{u}$ lies in Quadrant III.